Kamui is eager to leave Tokyo but reluctantly stays as Subaru asks and they reveal that when they arrived on that world, some sort of trap was triggered by their presence and they became separated by the magic of the feathers, with Kamui alone in on the outside and Subaru within. Since that day, Kamui has been protecting Subaru by protecting the water and by proxy, the humans living in the Diet building. With Fai dying, Subaru prepares to offer his blood to save him (as directed by Yuuko) when Kamui intervenes and states that he doesn't want anyone else to have a hold on his brother (this being a reference to Seishirou as it is strongly implied Subaru shared blood with him). In TRC, vampires are stronger, faster, and while they don't live forever, they live longer by aging more slowly, possessing a remarkable healing ability. It's clear that Kamui considers their task done with this but the twins stay long enough for Sakura to retrieve another feather so that the humans remaining on this world and the last of the water can be protected.
While not much is known yet about Kamui's past, it's clear that he is very possessive of his twin, as Subaru appears to be in kind, the two far closer than simple siblings and their relationship is complicated and deep. Kamui would not hesitate to kill for Subaru and while he appears to be the dominant twin from outward appearances, it is Subaru who can stop him with just a few words. He is also terribly jealous and fearful of what Seishirou's appearance may or may not mean in their lives, not understanding why Subaru saved him and ready to run as far away as possible if Subaru will not let him kill the man so that they might stay together.
Personality:
Kamui is ruthless, colder and more adept at surviving. With the world falling down around him, he does whatever is necessary to protect his sleeping twin (and as an accident the people he's living with). He is also more withdrawn, less apt to share his feelings except with Subaru and there he can't seem to hide them no matter how hard he tries. When Subaru is involved, Kamui is something of a force of nature, determined to protect and care for his twin, the only visible soft side the vampire has shown in Subaru's presence. The thing that Kamui appears to fear the most is being left behind by Subaru.