There are very few pulls -- and those are in early flashpoints where healing tools are very limited -- where you might not be able to keep a trigger-happy DPS AND the tank up. Hotkey your skills, don't click them, and you'll have an easier time keeping the whole group alive. You even have your AoE heal by level 49, no reason DPS should be dying even if they ARE impatient.
hot key or clicker play which ever method suites you the best. neither is worse than the other no matter what ex wow players say and think. a bad player is a bad player no matter if he uses a mouse or key pad.
as far as pulling agro when ever you put down your aoe heal any non taunted/attacked mobs will instantly agro to you. same if several are beating on the tank and you have him in the aoe, the dot on him plus any other heal. those he hasn't taunted nor keep taunting will soon be yours. it isn't your fault as much as the tanks and the dps to some extent too.