I don't know which quests you guys are talking about, but I didn't have any problems figuring out when to heal and when to DPS. Most of them with NPCs helping you are pretty obvious with the way they fight the mobs their level and one weaker mob equal to your level attacks you specifically. Only times I specifically remember healing NPCs were the quest in east shroud with tainted mobs coming in pairs at your pair of friendlies, the battle royale before the gargoyle fight, and the one before Ifrit. Even that one though, I think is more about surviving waves and if you take out the one that comes for you specifically and then heal a little before the next wave, you should be good.
The quest text and battle texts are pretty informative too. They usually give you an idea of how to beat the encounter either beforehand or during it. Otherwise stay alive, kill things killing you, and heal others in that order worked pretty well for me.
I did die once on the quest to save Biggs and wedge. The robot can nearly one shot you so you've got to stay topped off at all times. I was also pretty sure I was going to die like 5 times on the quest with the moogle above tam tara but he was clutch with his heals.