I added some zooanthids, waited a week, then rearranged the rock they were on. I think I was a little rough with them as I could see some "stuff" wafting off of them. (I had gloves on, thankfully.)
A couple days after that episode, I noticed a dark spot near the tail of my O.Clown. I kind of looked like the spot on your tang. After researching, I decided it was probably just a reaction to some toxin off the zooanthid - either it went over and tried to host in it, or a blob of the "stuff" that it released found its way to the fish.
I watched it closely, and it eventually just faded away. Like your tank, my fish ate fine during that period, but did seem a little less active than normal. It never developed a "fuzz" though, but maybe the coloration of the fish just masked it, unlike your tang. I didn't do anything to treat my clown. I did feed it some garlic with it's mysis though a little more often than normal. Other than that, I did nothing.
Perhaps your tang got a little chemical "burn" from the new corals?