one thing the OP is probably aware of, but many players who are new to this game are not (sometimes even lvl 50 don't know that):

you can see who has how much aggro on the monster. in the party window, below the job icon, there is a white bar and a number.

A full bar means, you have the highest enmity on the selected monster in your party. The other bars are filled proportional to that amount (if the healers bar is 30% full, it means he has 30% enmity of the party member with the highest enmity).

The number is the enmity order within the party. So the player with the number 3 has the third highest enmity. "A" means, that player is being attacked. A "1" means that player has the highest enmity, but is not being attacked by the monster. This happens mostly in fates, when someone from another party is being attacked.

Using this a DPS can make sure he doesn't take the aggro from the tank, even before it happens, because he can always see when he's too close to the tank and must tone down a bit.


On a similar note: Limit breaks don't generate enmity (at least the melee limit break doesn't, i assume it's the same with the others)