The tang likely does have ich, just in the gills. Without knowing how long the other fish are inthe tank before showing symptoms, I'd guess that the ich is in your setup, the new fish pick it up, the existing fish have low level infections that are not obvious. The new fish, already stressed, get worse cases, and the ongoing harrasment of the tang prevents them fro fighting the infection, so they die.
I'd pull the tang and chromis into quarantine, treat them, let the tank run fishles, raised temp, for aabout 4 weeks. Then add something similarly aggressive, like a dwarf angel to the main tank, let it establish some turf and get comfortable, then consider adding the tang and chromis back to the tank.
I'd pull the tang and chromis into quarantine, treat them, let the tank run fishles, raised temp, for aabout 4 weeks. Then add something similarly aggressive, like a dwarf angel to the main tank, let it establish some turf and get comfortable, then consider adding the tang and chromis back to the tank.