If my aiptasia had been that attractive I would have left it I think Mine was always nasty brown. How big is the anenome? It looks more like a flower anenome....but the picture could be deceiving.
Edit - ON second glance those tentacles look much longer than the flower anenomes I've seen.
To be that big and move that frequently, my bets are it's NOT aiptasia. Unless you were blasting it with a PH. Like someone else mentioned, check out rock anenome and flower anenome on the internet, I think you may have lucked out on this hitchhiker
By the way...that green algae is fun to get off the glass isn't it