Although the picture is not great, I would say it is Aiptasia. The rate it spreads kind of confirms that. The problem with Aiptasia is that they sting and kill other corals in the tank.
It should not be difficult to remove the rock from the tank, and treat it there. I had some once, and I just removed the rock and applied boiling water to the little bugger. That got rid of it and did not harm the rock. I applied the water to the Aiptasia without putting it on the rest of the rock.
Peppermint shrimp should also get rid of them.
