Hi!
By "chase the tank," I meant that I'm fighting for that number two (number three if the off-tank is good about aggro management) spot in the aggro list as a DPS. I actually don't fight for it as a red mage, partly because I'm usually red maging in situations where an extra rezzer is needed and partly because I actually suck at optimizing the red mage rotation.
On the jobs that I do, though, it's basically a matter of guessing at the optimal rotation for that job at that level and doing it as perfectly as I can. For example, on NIN, using Trick Attack (debuffs the enemy to make them take more damage from you) whenever it comes off cooldown and trying to fit as many of my strong attacks as possible into that debuff window, and trying to do this in alignment with everyone else's big two-minute party buffs. If I know the fight really well, I might even do things like hold my spare charge of Raiton for a mechanic that I know I'll be forced to disengage for, so that I can keep full DPS uptime even at range.
That being said, a lot of people in normal duties either don't know how to optimize their DPS or don't care - understandably, because most normal duties don't have an enrage. (and for the ones that do, you'll only see them if like everyone is asleep.) Very different from a savage environment, where this stuff actually matters. Still, it's very satisfying, and like. How could I, personally, play DPS and not try my darnedest to do ALL THE DPS
(fallen london stamps by