In Joon falling in love with Hae Ra has been subtle.  

In episode 1, Tae In Joon first met Hae Ra in a Noraebang setting. He paid no attention to her. In that social context, he would have passed her off a companion / escort of sort. He confronts obnoxious guy. Needing to pitch to the Italian business man, he asked for a translator. Obnoxious guy brought a translator but obviously would not have render assistance to a competitor.

Hae Ra volunteers her translation. A visible pause as In Joon is surprised that the lady was not here just for her looks. He pitches his proposal and willingly accedes to a inferior bargaining position as he expresses his company commitment to the deal. Italian dismisses him. In Joon protested that a verbal agreement was in place, and the Italian is to honor it. He threatens the Italian with future dealings. Hae Ra shares her insights that such threats are useless as the Italian’s leather is in demand. But In Joon asserts his opinion, and bluffs/boast his influence on the Korea market. Hae Ra shares this with the Italian but in a fashion that elicits his interest and for him reconsider his business partner.

Obnoxious guy is upset that Hae Ra ruined his business and splashed her with drinks. Tae In Joon expressed shock that another man (obnoxious guy who threw the drink) would behave in that fashion to a lady. He appears ready to intervene, same goes for the Italian designer. Both stands ready to save the damsel in distress. A different lady would have probably appeal to their chivalry. But Hae Ra shows her mettle, she bears the indignity, and empties the ice pail over herself, to lend excuse for leaving. Her parting words carries an undertone of her pride and character. This sparks interest in In Joon.

In Joon follows Hae Ra and grabs her wrist, surprised that her calloused and discolored hand. Hae Ra is flustered that a man grabs her wrist, both out of embarrassment of her hands and In Joon’s audacious action. In Joon proposed a business deal that Hae Ra works the Italian, and insinuate it be done through favors. Hae Ra is astounded at his rudeness and confronts the meaning of his words. In Joon brushes the question aside and pushes forward money. Hae Ra is insulted, smirks and rejected his proposal.

Perhaps in In Joon’s world, a chaebol is always surrounded with pretty girls who would bend over backwards for money. He sees Hae Ra’s refusal as a bid to extort more money. He challenges her that the payment was fair and finally voiced out his impression that Hae Ra was an escort. Insulted, Hae Ra slaps him, telling In Joon that she has helped him thus far because she empathizes with him and In Joon reminded her of her unfortunate circumstances. That she put up with his past transgression because she pities him. The insult of being viewed as a common whore brought out her anger and Hae Ra avowed that she would prevent his business proposal with the Italian. In Joon can be seen to sign in frustration when Hae Ra walks out on him, that he might have been taken wrongly by her.

He chased after Hae Ra and strongly assisted Hae Ra into his chauffeured car. In the car, he demonstrates that he has always knew that Hae Ra was no simple lady from her calloused and discolored hand, that he knew Hae Ra is associated with leather works.  He continues talking down to Hae Ra, despite needing her help. In Joon remarks that he is willing to forgo the business deal if Hae Ra would not misunderstand him.

Hae Ra remarked that she’s unconvinced of his sincerity, and hints that she is still angry that In Joon had thought that she was a prostitute. In Joon tries to brush it off as joke that he had meant no disrespect that he had not consider himself to be her better, that if she is a prostitute, he was no better as he sells a different part of himself for work (his dignity, bearing insults from obnoxious guy just to pitch his business deal).

He tries to play it cool by offering to send her home, seeing that Hae Ra is still upset at him, In Joon apologizes. Seeing that Hae Ra smoothen at his apology, he apologizes again, formally. In Joon had been using informal speech with her all this while, but had formally apologized, demonstrating his sincerity, and admitting that Hae Ra is his superior. (Expression in speech conveys status between the participants. Informal speech hints of status difference between the participants, and from higher to lower or between equals).

Hae Ra is surprised but accept his apology. She made a offhand comment that he had been forceful and bullish. Hearing that In Joon tries to show that he can also be thoughtful of others, by requesting the chauffer turn up the heat in consideration that Hae Ra may have been cold due to her wet clothes. Appreciating the gesture, Hae Ra expresses concern over In Joon’s job security should the business deal with the Italian not worked out. She did so in a nonchalant fashion, to appear collected over In Joon’s gentlemanly gesture of turning up the heat.

They ride the rest of the journey in silence, so as to appear casually calm with each other, with neither wanting to concede that they may have been concerned with each other. When they arrive at Hae Ra’s place, Hae Ra tells In Joon how to better his chance with the business deal, through a roundabout question. She gets off the car, leaving In Joon gazing at her back.

The chauffeur drove off, but returns shortly, just in time for In Joon to witness Hae Ra’s house being trashed by gangsters. When the chauffeur / secretary could not understand why In Joon remains in the car, despite him being obviously concerned with her, by turning back the car. In Joon get defensive. Perhaps owing to his chaebol background where people deceit and purposefully approach him for money, he questions how he should help her, and with money how much. (this hint of the transaction relationship he had always developed with people in his world.) He seems genuinely surprised that Hae Ra had been truthful with him, and at ease that Hae Ra is indeed a shoemaker and not a prostitute which he had initially mistaken. As he reflects on their short encounter, In Joon recalls her watch when he held her wrist in the car, and commented that it was a nice watch, although it is spoilt. He must have paying plenty of attention to her, to had glimpse that detail.  

In the parting scene, against conventional wisdom demonstrated with the secretary, In Joon chose to risk his business deal falling through and trust Hae Ra’s judgement in securing a boy band’s autograph that promised to facilitate the business deal.

It is this moment, that I think In Joon first fall in love with Hae Ra.

@swongy—Thank you for recapping the nuances of the first interactions between Hae Ra and In Joon. I've found their attraction compelling from the start. In Joon doesn't have much choice, given their potent mix of fate (real and fake), easy intimacy, shared passions and general optics. As you noted before, her eyes alone are enough to make one swoon. And this bit cracked me up—until I read your post, I didn't understand why In Joon turned up the car's heat. Well spotted, @swongy!

It's so interesting how perceived "chemistry" isn't a universal given. Psychologist, director and former actor Pamela Stephenson Connolly argues that the audience is as essential to creating chemistry as the actors themselves:

"The truth is, each audience member projects their own, particular, deep-seated longing, lust, and love-aspirations on to whichever couple displays the right character, appearance, behaviour, situation, and relating style for their individual tastes. They are part of a three-way relationship: in a triangle with the two actors." (The Guardian: The sizzling secrets of on-screen chemistry: from Dirty Dancing to La La Land, 24 Nov. 2016)

I would expand that "three-way relationship" to include script, director and production elements as keys to creating chemistry too.

I find In Joon unlike any chaebol character I've ever seen. He's a bit of a beta—not aggressive (unless provoked by his horrible family), generally decent and owns little outside of his car and glorious suit collection. Does he own his condo? I hope so.

Characters and viewers alike chastise him for being stupid and lacking business sense. I'm hoping he's not as naive as he appears but I've got three arguments to support In Joon's actions:

1. K-drama revenge is a long game and he's tired
He's been planning revenge for most of his life, since his father kicked him out at age 12. (I think his character is about 36 years old.)  Yet once things are finally coming together, revenge brings him little joy. In fact, he feels worse. 

Once he saw that gains against his father are easily reversed, he likely calculated that the contract marriage will only bring him misery without the hoped-for coup against his father. 

His ability to shake off the sunk cost fallacy is not idiocy—it's brilliant and incredibly hard to do.

2. Expanded core values
Until Hae Ra disrupted his life, his core value was filial piety towards his deceased mother. But rather than living well in her memory, he spent his adult life plotting revenge in her name. He's quite brave to refocus on positive actions such as opening his heart to Hae Ra and building the shoe company without prostituting himself.

Realigning his core values to be happier and healthier reflects his emotional intelligence.

3. A deal with the k-drama devil
Completely handing his stocks and management rights to his trash-bag brother is crazy but he probably saw it as the best way to cut himself from his conglomerate burdens. 

Okay, I'm pressing the melo-melo-ignore-suspend-belief-button. 

I think the most likely of all reasons, is that In Joon as with a multitude of preproduced korean drama characters suffers from the lack of a concrete script. Each drama episode was filmed in a live shooting format, with the filming of each episode perhaps leading the release by mere days. While live shooting the drama, allows the script writer to take real time feedback and act upon it, revising the script as required. It inadvertently meant that the cast started only with a skeleton script or a proposed script that can change in real time. 

The trouble is manifest when the audience feedback disapprovingly of the character/ drama and the script writer is required to revise the character. This can result in conflict of personality portrayed by the actor, especially when they had envisioned a different character than the one necessitated by audience demand. 

In Fates and Furies, maybe just maybe, the script writer needed to hasten the drama, and kicked off In Joon and Hae Re romance / post romance, that they had unwittingly reduced In Joon into a hopeless business man  drunk on the illusion of love. 

But its all okay in my opinion. The only critical thing I need is a good looking actress and I can settle for subpar storyline. I have completed worse drama with retarded story lines and unrealistic characters. The girl made me stay and that's why they are A listers. Go Lee Min Jung.