You should be safe after qt. Ich is a parasite that swims in the water, and attaches itself to fish, sometimes in the skin, sometimes in the gills---the latter is where it can come in undetected if you're not used to the species and don't pick up the signs of swollen gills or slight flaring or hanging near the surface.
The life cycle is about 6 weeks. Think of it as very like a flea infestation: if you eliminate the parasite and kill the next-gen hatch before they lay eggs, you're clean.
Tangs have the following characteristics: fast, strong swimmers, need a long run; aggressive toward other pancake-shaped fish, at worst, mostly toward perceived rivals or threats---my allegedly highly aggressive purple, [to go back to the store next week] has been a good guest with the cigarshaped fish I have: he couldn't hit one on a bet and they don't threaten him, and he never attacks, but he scares the daylights out of them with his strong movements. Second, they don't have scales: this lack of armor coating and lack of slime [such as mandarins have] leaves them unusually vulnerable to ich---they're more open water swimmers, and our shallow tanks force them to be much closer to the substrate [where one stage of ich lives] than ever happens in nature. Third, they have a very, very high oxygen need. Tangs get a rep for being the first fish to die in a tank crisis: this is often because of an oxygen lack.
They also get a disorder called hlle, or 'head and lateral line erosion', which is an ulceration in those areas: this is thought to be a dietary deficiency---too much meat, too little green algae. My purple came to me with hlle. I found that this little beggar despises nori, won't touch it on a bet, and he'll go for the meaty foods every time. So his previous owner probably indulged him, fed him only the chocolates, and turned him in when he got the hlle. I found he WILL eat Formula Spirulina cubes, which are strongly flavored spirulina algae mixed with chopped squid and clams, and this is improving his problem. But he's not for a 54, alas, and now that he's done in my caulerpa problem, he'll go back to the lfs in search of a big new home. His hlle has healed considerably, and if his new owner can feed him his spirulina cubes [which I will recommend to the lfs owner] he will continue to improve. HTH. Sounds like you have a great tank for a hippo.