Those are definitely vermetid snails. As others have indicated, they can spread like wildfire if the conditions are right in the tank. They are filter feeders so broadcast feeding particulate foods will exacerbate their spread.
Once they're in the tank, they're very difficult if not impossible to fully eradicate. Typically you have to manually remove them, making sure you get the base crushed or completely removed. However, they can grow deep in the rockwork where you can't get to them and can also grow inside your plumbing despite the absence of light.
Some people have success using bumblebee snails which supposedly eat them, but your mileage may vary and typically you need a lot of them for it to work. It's certainly worth a try. I have several bumblebees in my tank but they really don't make a dent in the overall vermetid population.
I eventually gave up on trying to remove them as they spread too quickly. To be honest though, they don't really bother my corals. They're just an eyesore as they cover the rockwork and make it look like a pincushion. Occasionally, if I see one nestled in between some zoanthid polyps or on LPS skeletons like your picture I will remove those, but I don't really worry about them otherwise.