Your anemone will only move if he doesn't like where he is. I put my H. magnifica anemone on a rock in the middle of a sandy area, and they don't like sand much so he stayed put. However, I went for about a month without light at one stage and he climbed up the glass right to the top of the aquarium to try and get more light. When I got my new bulbs I put him back and he stayed put again. Anemones generally seem to like high lighting intensity, no less than 175-watt Metal Halide or they will not live (except perhaps VHO or PC), I have mine under 400-watt Metal Halides.
Regards,
Tom