First question what kind of carpet anemone? There are several different carpet anemones with different requirements.
A haddoni which is a carpet anemone placed on the rock will move to the sand. A haddoni with no sand will move because they need a deeper sandbed.
Now a gigantea which is a carpet anemone like the rocks and wont move to the sand.
There are others too.
It makes a difference because most of the time they move because they do not like where they are, they really do not move much if at all if they are happy..
Should you be concerned? maybe.. If he is happy and getting what he needs there he maybe fine. Now if he is not getting any light probably not good.
Was the anemone bleached?
Most anemones hide in the shade if they are getting more light compared to what they are used too. They may acclimate themselves and slowly move out..