According to the rules:
You must successfully cast a conjuration (healing) spell on an ally after being hit by an attack of opportunity, or have the Battle, Chaplain, or Healed background.
So I take this to mean after you've been hit by an AOO, not the ally, correct?
And is it immediately after, or during the same turn, or battle, or session? The text implies it can be anytime after the hit, e.g. years later would still count.
Completion Benefit: You automatically succeed at concentration checks for conjuration (healing) spells caused by taking damage.
I assume this means that if you have taken damage while casting a healing spell, then you automatically pass your concentration check, correct?