Okay, I'm no expert on the Buffyverse, but the way I understand it is that if a girl has the potential to be a Slayer, than she is a potential Slayer. It only makes sense. The girls staying with Buffy were not all of the potentials. There were still more out there, like the girls seen being activated during Buffy's speech. If every girl had the potential, every single female in the Buffyverse would have gained Slayer powers. Willow, Fred, even Harmony would now be "chosen." Girls become potentials when they become teenagers, and if they are past their prime when it's time for a new slayer, they will be overlooked and a more young, fit girl will be the next slayer. But the spell in "Chosen" activated the dormant powers in every one of the potentials, which is why some of the women may be older. There may be some 80 year old women out there whose dormant powers were released, giving her extra abilities. It really doesn't matter the age anymore.
Newborns wil most likely only gain their abilities in their adolescence, however.
But then again, I'm no expert....