light will indeed make them move if they arent getting any they will move to where they are you wont see many bubble tips hiding in the dark if theres light to be had, now im not saying its the cause but there are a number of things an anemone needs and light is def one as is water chemistry and flow.
bubble tips are active movers and can be found moving around alot they are also active reproducers most people who have bubble tips know that it isnt uncommon for them to split constantly and the first thing a split nem does is go for a walk looking for a place to feed and then do what it was meant for....reproduce again
beautiful species