Well it's neither Anemonia majano nor Aiptasia mutabilis, but I don't know what it is - i've never seen it before. Searching the net for "tulip anemone" didn't help, it's identified variously as Anemonia and Aiptasia, which it isn't, or at least no species of those genera I've ever seen.
The uneven foot suggests that it reproduces by pedal laceration, but if they haven't become more than a dozen in "years" it doesn't seem as if it's a pest. Also IMO it's somewhat attractive with that unusual shape, I wouldn't mind having one.