(Huh? Forum just ate my post? Ugh.)
Yeah, it is as you say. Healing abilities are used automatically at the end of your turn. The way it works, according to the official forum: first it heals the leftmost unit in your lineup. If that unit was only slightly injured and didn't require the full heal, the leftover points are used to heal the next eligible unit, and so on.
(Some abilities seem to work differently, like heal undead which I may have read heals the most injured unit instead. I'm not sure, haven't tested it.)
I would love an AoW1 style active ability too. Not only does if afford more control, it makes more sense: now, if I can get in an easy fight, I can use nets and whatnot to stall for ages while my priests heal everybody. But at the end of the turn, you can only use the ability once. Weird.
Ah well. On the plus side, at least you can't forget to use the ability before clicking "end turn" anymore.