[Endoperez]

Affecting dominion is taken at the start of the turn for stat/hp -modifiers of pretenders and prophets, and I think although I am not sure that for immortality only the dominion at the end of the turn matters.
First one is easy to try out: attack with your pretender from positive dominion province to one with negative dominion, and you'll see he has bonus to hitpoints (and other things), but I don'tremember where I read the latter 'fact' about immortality&dominion.