If you recently added a fish then the spots could be some sort of parasite or disease, but if you periodically feed food marinated in a drop of Garlic Oil without added water(5 days straight for new fish), then it's probably not a parasite.
Sometimes water/tank conditions can cause disease.
What is the Alkalinity?
Is water moving well from bottom to top of tank, rolling at the surface?
Is there plenty of Algae for these Tangs to graze on?