SE population minister works this way :
-- It moves population only to "native" atmosphere planet. That is if you are oxygen, no methan planets will ever receive any transports
I do not know what will happen when you capture homeworld of another atmospher race. I suspect it will not move them though.
-- In every moment there is only one "target" planet to get population, all transports are always directed to one particular planet. According to my observations, it is the closest planet with native atmosphere to homeworld.
-- Sometimes AI turns transports back. Ships must have about 150% supplies to make round trip. Otherwise they will be caught in silly "resuply" loop without moving any population at all.
-- I still do not know when AI decides when one planet get enough people and switch to another planet. I suspect it is when "population bar" is filled up to 2/3