Mushrooms will spread like that as well, and I have never seen/heard of red aptasia, but a picture would probably clear things up. You could try 'pruning' about 50% of the mushrooms off the rock they are on, then placing them in a shallow dish of crushed coral covered by netting for a few weeks until they attach, then gluing them to rocks/shells/plugs and selling/trading them. If the mushrooms have room to expand on the rock they are on, they may stop dropping off to spread? (This is a theory, but it seems plausible.)