I have also treated Ich with using garlic. It's fast, safe and will help boost the the fishes immune system. For the tang the best way to get garlic into them is with Nori seaweed. Just place a few drops onto the seaweed let is soak in and then clip it to a veggie clip and place in tank.
Also have you thought of adding a Cleaner shrimp to the tank?
One thing to keep in mind with Ich it will reoccur if you have not found what caused it in the first place.
So you should ask yourself a few questions...
Temp stable?
Water parameters in check?
Feeding the right foods? Tangs need plenty of veggie matter and seaweed to stay healthy.
Any aggression in the tank causing the fish stress?
Purple tangs are notorious for getting Ick but with the proper diet he should do just fine.
I have never QTed a fish with Ich or have ever recommended moving one that has already been placed in the main tank...the stress of the move only makes matters worse. I have always recommended treatment of garlic and treating the fish in the main tank.