Anemones like Aiptasia species can often lurk in the rock for a while and surprise you when they finally pop out, although the purse-closing appearance in the top pic is a tad odd for an Aiptasia species. Balls on the ends of the tentacles are also a bit unusual (although doesn't have a distinctly Majano look to it either to me, but I haven't seen as many of them).
Be careful taking it out if you want to preserve it (at least until IDed). Anemones that have stuck themselves onto something are easily injured by being pried free, even from a surface like glass.