Under you first lights the Bubble tip will likely get smaller and smaller until it is gone. It will get used to the new lights in no time at all and they will help it thrive and grow. As with all photosynthetic animals it needs the brighter lights. Power compacts are about the minimum for good health in a reef tank.
Anemones will sometimes shrivel up as you described for seemingly no reason at all. They are simply resting and often times excreting. Look at what your other corals do at night. Most of them shrivel up pretty small too, especially the mushrooms. There is usually nothing wrong with them and they will be back to their usual beauty soon.