"Fin rot" or the appearance of wasting finage can come from many sources. The two most common being water quality and aggression. Feeding and "sleeping" areas can also come into play.
Considering this is a new addition that just went through QT and a treatment (?), stress is also a factor. I realise you say your water quality is very good but please post what the actual numbers are for ammonia, nitrite, nitrate, pH, salinity and temp. The more information you provide, the more accurate the responses will be.
Are the nips areas on the fin clear or cloudy, any sign of a cottony substance or redness?
When the tang beds down at night after lights out, where/how does it sleep?
What seaweed are you feeding and how often/how much?
What tank mates including mobile inverts?
Are you providing the fish with extra vitamins, HUFA or related items? Beta glucan, Zoe, Selcon and the like?
I would right away suggest you get a good amount of SW ready for some water changes. Large water changes are often the best first step in fighting/preventing problems of this nature from taking hold or getting worse. Lowering potential DOC no matter how good the water quality is, is the best first line of defense. Try to prepare enough to do at least 3x20% water changes over the next 5-6 days.
Cheers
Steve