I don't know what kind of anemone it is, but do know red anemones do exist, but are very rare. I've only seen two in all the places I have been diving, one was on a wreck in Truk Lagoon, the other was in the Red Sea, both were very large.
I did take a couple of pictures of the one in the Red Sea, will try to find them and post them for you.
divedog