I was trying to get my powerhead pointed to another direction, and thought it was part of the rock when i was looking at the water from above the tank so i just grabbed it to move it a bit then felt the jelly feeling and dropped it quick.
No, zoas detach and just float to a new location, but nems will actively move. Im not sure what type of nem that is, but it would remove it before it can become a possible pest
If it actually moves around your tank I'd try to frustrate it enough to detach and then isolate it for a better ID. Before reading anything I thought it looked like some kind of Paly