Yeah, some things that can impact a fish's coloration (leaving a few irrelevant factors out of the conversation):
-Light (wavelength, intensity, and duration)
-Health
-Diet (including both vitamins, minerals, etc. and pigments like astaxanthin in a fish's diet)
-Various chemicals and hormones
-Genetics
Some things that affect a fish's coloration are immediate (like stress) while others (like lighting and diet) can take much, much longer to make a noticeable difference. It's possible that this tang's coloration is a result of some of those less-immediate factors, so it may take a while for it to change.
For the diet, I'd recommend the following, preferably supplemented with algae (most people use nori, but the more algae/kinds of algae offered to the fish, the better; fresh/frozen is best, but the pellets below are solid brands):
(I apologize, I haven't looked into frozen algae-heavy feeds enough to have one that I would suggest at this point; I'll have to remedy that):
Frozen (Meaty) - LRS Reef Frenzy, Hikari Mega Marine, then Rod's Original.
Pellets (Meaty) - Otohime, then TDO Chromaboost.
Pellets (Algal) - NLS Marine Fish Pellets (has 8 types of algae and one terrestrial plant).
For an example of the difference pigments in a fish's diet can make:
https://nhrec.org/wp-content/upload...ture-astaxanthin-level-average-preference.pdfFor an example of the difference that lighting can make:
https://www.reef2reef.com/threads/does-lighting-affect-your-fish.1012917/