Saygo :
transmigrates into a another world through through a story (ie tv, book, script etc)
So not just teleported through time or something, but it has to happened through reading/watching a story?
Mr. Queen and Moon Lovers didn't involve a story, it was time travel under special circumstances (near-death and a solar eclipse). I don't remember a story involved in The Eternal Love.
Would Extraordinary You count if they were always characters in a comic, they didn't get transported there?
I will leave it to the poster to decide, but I don't know if you have seen them so just asking for clarification.