Yes, that is an aiptasia, and yes, you need to take steps to make sure it doesn't spread.
In your case what I would do is remove the frag to a small bowl of tank water so that you have easy access to it. Then, after studying it carefully so that you know exactly where the pesky little bugger resides, take the frag out of water, pat the area fairly dry, use tweezers or a hemostat to pluck as much of it off as you can, and then use a small (TB) syringe to soak the immediate area in hydrogen peroxide. Allow the H2O2 to stay on for 5-10 minutes. then rinse the frag in a little more tank water and return it to your tank. Keep a close eye on it for a couple weeks to make sure you got all of it.
The other option would be to do what I do in my tank when they pop up (and they will, regardless)
I use a 10ml syringe with a 18g blunt needle filled with boiling water to cook the little devil in place. Because of it's close proximity to one of the zoanthid polyps you may lose that polyp but they grow fast. After using the entire 10ml to cook it, place the blunt needle directly on top of any remains and draw back hard on the syringe. You will suck the remaining tissue up into the syringe and you can then toss it in the trash.
hth!
