I think your tangs are eating algae from the gorg. rather than the gorg itself...although with tangs, you can never be exactly sure! I have a foxface in with my gorg, and he does not bother it all.
Preferably they need high flow and low light to discourage algae growth on them. From what I have read (and I am no expert on these) they eat very small particle food, like rotifiers and Golden Pearls. In order to be healthy they need:
(i) the right size particle food;
(ii) delivered to them at the right speed (high flow - somehwere around 8-12 cms/second);
(iii) no algae growth on them; and
(iv) a very constant supply of food (ie - a slightly "dirty" tank, or else, a "clean" tank with a ton of feedings).
Take all this with a grain of salt, as I do not think anyone truly understands this coral.
I have read that they do better in non-SPS set-ups as the water is generally less pristine in a non-SPS tank...but that is a huge generalization (there are some very "clean" softies tanks). They are a lot of work, require the correct placement in a tank, and they require a lot of feedings as described above...even then, they do not survive that well in a home aquarium. The worst news is that they often look like they are doing well, but in reality, they are starving to death...and then one day they just implode, and start falling apart. Make sure you try to feed it a bunch of different types of the correct particle food.
That said, I have one too, so I am not flaming you for getting one...they are truly gorgeous corals...but please do not fool yourself, they are a pretty hard coral to keep.
HTH
Stewart