Paul: I think the rules do explicitly say that at the top of page 11:
"...place 1 of your 6 available influence tokens from your supply onto the map on the lower left of the board and immediately gain the benefit listed below the name of the region."
They go on to say (in reference to moving influence stars within the map after you've already placed them there): "You don't gain any immediate benefit from moving a star--you only get the benefit when you place a star."
Thanks for clarifying Jamey. I read that and assumed it would be like you explained, but I found it contra-intuitive when comparing to other game that typically give a bonus to the first to come in these situations. So just wanted to double check I did it right.