It sure looks like a basic rock flower anemone. They, and many nems, will shrink for a lot of reasons, mostly harmless. They don't like bright light, possibly why yours moved. Mostly they seem to hang out in shaded areas. They're also common in the waters where Tampa Bay Saltwater has their live rock leases, so it's expected to get one or more from them.
Some people hate these, but they're really easy to care for. They eat any of the frozen foods, mysis, pieces of clam or shrimp, etc. They need iodine dosing if you don't do frequent water changes, but that's about it. Not spectacular, but interesting.
Jeff