Mysterious round white coral-like growth (magic!)

Hi all! I went on vacation and returned 2 weeks later my salt tank had 2 mysterious growths. I have no idea what they are or where they came from and therefore if I should get rid of them.
Strange growth: There are two round, white, fleshy, independent and separate growths on the bottom side of one rock. They feel like soft coral; not slimy but slippery. They give under my finger but I can't smash it all the way down to the rock either. There appears to be a puckered mouth in the center (similar to the mouth of my mushrooms Actinodiscus sp.). One is about 1 cm thick and 4 cm diameter, the other is also 1 cm thick but only 1 cm diameter. When not touched they appear almost porous. I've seen no tentacles, protrusions, fins, feelers, etc. I cannot find anything online except that they look like a plumose anemone when fully pulled in, however no tentacles have ever appeared in night or day.
My tank: I've had the tank since early December, it was bequethed to me with a hand full of life in it. I do not know it's full history. I currently have mushrooms(Actinodiscus sp and Discosoma neglectum), zooanthids, pulsing zenia(Xenia umbellata), carnation (Stereonephthya sp), hammer(Euphyllia paranchora), bubble, tongue and Lord acan's (Acanthastrea lordhowensis) coral. There have been no new additions of coral or fish for 3 months.
If I have forgotten any necessary information, please mention. Ideas?