As a tank, I say as long as priority #1 is being satisfied -- that none of us are dying/close to dying and you're aware of the party -- I say girrrrrrl, you deal that damage.
I think this goes more into the need for tanks and healers to be especially communicative, as much so as possible. Each should set expectations of the other so that surprises are minimized. Like, for instance, I'll tell the healers when fighting Ultima Weapon that when he hellfires the party, I'm going to pop my hallowed ground cooldown so that there's no chance of me dying, which means they can focus completely on the rest of the party without worrying about me so everyone can be back on their feet as fast as possible. Or, with Garuda, I'll tell the healer to focus more on DPSing the plumes to take them out faster, and that I'll pop a cooldown or two to stay safe without having to worry about me during those 15-20 seconds. Build the tank-healer relationship, if possible, and issues like what happened to you in AK won't happen, or at least have a way smaller chance of happening.
