Mine don't budge. But its possible they can move if they are annoyed by the new water.
Do you have a sump? Are you removing and adding the water to the display tank?
If you have a sump slowly drain the water from the display and don't let air hit the anemone. Then add saltwater to the sump that's been mixed, sat for a few hours to 24 hours, temperature and salinity matched. If you are adding colder water it could move due to that. Or if you are adding water in real fast and causing turbulence that annoys it.
If you don't have a sump do the same but slowly, very slowly add it back into the display tank. Be sure the temp and salinity match and that it wasn't just freshly mixed.