Is it attached? It really looks like a small Fungia plate coral. They have a stony skeleton underneath, but their normal state is very inflated. They can deflate very, very quickly. It's hard to see in the picture, but the mouth on a Fungia is usually a straight line rather than round.
It definitely doesn't look like a Duncan. Duncan's have a flat oral disk with a ring of tentacles around the edge.
Some mushrooms can have those distinctive ridges with the short pseudo-tentacles. Some mushrooms are also faster than others to react to stimuli. There is even one mushroom that eats fish. So the speed of retraction does not totally rule out that possibility.