So the Archon eidolon "At 8th level, archon eidolons gain the ability increase evolution, applied to an ability score the summoner chooses."
Does this count as and follow the rules of the normal evolution? meaning if that is going to str does it count as 1 of the 2 increases I can do or is it separate from all the choices I make with the evo points?
It's a free bonus evolution. It's still subject to the constraints in using it. So I think it still counts, but you are getting it for free.