took falling damage during a fight. My cleric is still showing max health 19/19, but there are 2 health bars, one mostly empty (should be the accurate one because i did take damage).
Not sure what Rally is, but I did not take any kind of action to give myself temporary hit points. Also 19 is my normal max, so if I had temporary hit poitns wouldn't that number increase?
Rally is the little flag buff that you can see above the health bar in the image. It's an ability that fighters get, but I think the horn by the gate to the druid's grove applies it as well. As for max health increasing vs secondary hp bar, it just varies per ability e.g. cleric spell Aid works like you described, but warlock passive Dark One's Blessing also gives a secondary hp bar.