Is the "Health on kill" gem bugged? Getting health on damage dealt instead

Im curious if its a bug, or a wording error, and if anyone else has this happening. On my regular short bow, not enchanted, I have the health on kill gem, stamina on damage dealt gem, and focus on damage dealt gem all slotted in.
I dont have any other equipment that would give me health during fights, but I notice when I use my bow, Im gaining health with every hit. I used my enchanted sword that has a “health on kill” effect (not gem), and when I use it, I dont get any health during the battle, but after the fight I gain a good chunk of HP. Although when I use my short bow with the health gem, Im constantly getting health regen with every hit, and the indicator is showing up along with the stamina and focus to indeed show that Im gaining HP with every hit.
So is the gem misworded, or is it a bug?