Dominion spreads throughout all friendly and enemy provinces through a process called "temple checks" and is represented in-game by the number of candles in each province (yellow for friendly dominion, red for enemy dominion). Each Pretender unit itself generates an automatic candle every turn in the province they are in, plus initiates two temple checks. Prophets generate temple checks, as does the capital province and (not surprisingly) temples themselves. Temple checks are based on the current maximum dominion, so a dominion of 1 means a prophet only has a 10% chance of generating a candle, while a dominion of 9 would have a 90% chance.
Enemy dominion (red candles) affects your lands, and slowly converts the scales in a province to that of the nation whose dominion holds sway. Enemy heat/frost, growth/death, order/turmoil, productivity/sloth scales all affect your provinces per normal. Enemy drain scales also affect your provinces per normal, however enemy magic scales only apply the -1 MR to any friendly units in the province, but will not apply any research benefits.