The reason why coral appears to fluores under actinic light is because our eyes are not sensitive to light in UV spectrum. So our eyes dont "detect" the source light from the bulbs (that is why they look dim, whereas in reality, they are as bright as any other bulb) but the florescent proteins absorb the light in UV spectrum and emit it back as light within visible spectrum (like green). So the background light appears dim to our eyes compared to what is being fluoresed. Under white light, same effect doesn't occur because background light no longer appear dim to us. You can still see them fluores, but the effect is much less impressive because it gets washed out. You can imagine this as watching TV in a dark room, vs watching TV with sunlight over the TV.
I assume to corals that fluores under actinic light doesnt look that impressive to animals that can see into UV spectrum, such as birds.