My guess would be that this is a little tet-a-tet to stake out the 'pecking' order in the tank. Particularly if the clowns and the tang do not have enough room/LR
/etc. to specifically claim some territory in the tank. Sometimes if you introduce 2 tangs (of different types), e.g., a Sailfin and a Naso, for a least a little while they will sort of flap their bodies together in a display of 'power' (I use this term loosely and in the absence of a better term). Generally this is harmless.
On the other hand though, I have a Naso tang that I believe is a downright character. I'd swear this guy is thinking a lot more than what would be logical. At times he'll eat right from my hands and if I drag some seaweed around the tank he will chase it down in an almost playful manner.
Generally, I think one of the reason to collect SW
fish is that they have a tremendous amount of 'character' (also for lack of a better term).
One MadNucleus to one MadMan