@Não Sei I read the novel, but it was a long while ago so it might not be accurate, but heres the big spoiler:
I'm pretty sure J has white hair because of the result of the apocalypse, where J is slowly becoming more of a monster and less of a human. He dyes it regularly after he woke up from the West Sea Rift. I think it only started changing colour when he was stuck within the dungeon. The apocalypse is a result of this world's timeline colliding with the world we saw in Yoon-Gaeul's fragments (i think...?) and it makes the outside world's enviornment become similar to what we saw in the dungeon they just went in, with the white snowish substance floating down and the desolite look.