First time healing (AST) - what should I know?

[Risvertasashi]

One more quick tip I can think of:
Check if your tank is level synced and in sync'd gear. If you happen to get a true newbie tank that maybe doesn't have the greatest gear, stuff in some of the leveling dungeons can hit a lot harder than you might suspect. Brayflox's and Dzemael, for example, really punish tanks (and actually healers too) for being behind on gear.

Apart from Luminous Aether, is there anything else I can do to reduce aggro? It seems like whenever I heal, it draws monsters to me.

Your stances reduce aggro as well, so don't forget to put Diurnal up (and level syncing removes stances generally, so watch for that). Try not to overheal. Time your HoTs (i.e. aspected benefic) so that it falls off the tank before the next pull.

Of course, at some point the tank needs to established aggro. If they're not hitting some mobs in the pack then... as soon as you heal, they'll go for you. This can be a problem in FATEs too, by the way-- Not that they're very popular right now but for future reference.

I have one of those annoying "Hey stuff's hitting me tank pls take aggro" sound macros for those kind of situations xD