From my experience, I have 2 theories...both are directly related to each other
My first guess is stress. Fish don't like dramatic change or being picked on. It raises their heartbeat and breathing. It makes them more prone to illness like Ich. This could be caused by tank parameters or other fish. It's possible the clowns may have picked on it. Female clowns are particularly mean. Ask anyone that has a mated pair of clowns, they will defend their turf ferociously. And though their bite may not do much damage to us, it can really hurt a fish. Are your clowns Clarkii's? They are terribly aggressive!!!
My second guess is that the tank did not fully complete the cycle. What is your test kit? Some are obviously better than others (I prefer Elos). The tang probably was unable to handle the dramatic change of the system and simply dropped dead. Such things happen, but most of the time it can be narrowed down to stress. Clowns are super hardy and I'm willing to bet they could survive such distress (granted I would not want to test this). However, I do agree with the others, sometimes the tests are misleading (it happened to me with my first tank). A month is a good rule of thumb for a cycle. If you're starting from scratch, I normally add inverts at week 2, chromis at week 3 and normal fish at week 4. I normally wait to put in show fish at the end of month 2.
The exception to this is of you already have 50% (minimum) of cycled water at your disposal. In my case I already had a 45 gallon tank that I transferred directly into my 90. I threw in 6 frozen shrimp and let them rot for 2 weeks. Added inverts after 1 week, chromis at week 2 and normal fish at week 3.
You will discover patience is a virtue in this hobby. Keep an eye for extreme changes, and space your modifications over a series of days. Too much too quick only leads to stress. Thankfully it was only a yellow tang this time and not an achilles tang.
Good luck and happy reefing!