Corals will acclimate to their environement. If a frag is under certain lights and has become acclimated to that lighting, flow, nutient levels and it is moved and subjected to a completely different system, this frag then undergoes a complete systematic acclimation to another system. The frag will then have to become acclimated to your lighting, flow, nutrient levels etc before it can start to grow again.
Whether your lighting is different from where the frag was or even the same the frag will still either loose some of its color, all of it's color and after reacclimating to your system return to the color rendition it was or different depending on your lighting, flow and other system levels. Frags or corals under certain Kelvin rated lamps will hold that color usually but I have noticed most will increase coloration under 10k best. {Thats why I'm switching}.
You can usually tell if the frag continues to loose color and is doing so in a bad way. Polyps will withdraw, color becomes very dull and then bleaching will usually occur.