The HP raise is like Divine Grace, it is not Healing. And if you put this on him, he uses it over Brave Presence, which would make him NOT gaining any Hate and risk your other DPS getting killed first turn.
I think you might be reading it wrong.
It says it increases max HP and restores that amount HP. (as in once) - then there are 3 turns of TP regen.
Does not say there are 3 turns of HP auto-recover, it does for AP
Its a pretty meh TMR - the stats aren't amazing.
But good thing about the TMR is that the HP boost/regen is 30% at lvl one.
Ends up being a good chunk of HP on a tankier character for no investment into the skill. Also it is great for increasing the damage on a "Drain force" build