Ok, I've figured out why this happens.
# We will only reload weapons that the attacker is on the level for
if weapon != gungamelib.getPlayer(attacker).getWeapon():
return
That section seems to be responsible for the problem. I haven't confirmed it by removing it from the code yet, but I will try it out tonight after my clans server empties out. The problem seems to be that since this is tested after the player levels up, the gun they got the kill with is not the level they are on any longer. If you have turbo mode enabled, this is never an issue since you immediately go to the next gun. If you have multikill enabled, your gun is reloaded every time you kill someone until you level up, then it stops working, or turbo mode gives you the next gun. The variable this replaced made it so your gun was only reloaded when you leveled up, and not just when you got a kill with the gun for the level you were on. It seems like maybe I should ask for a custom addon since this addon really doesn't seem to be intended for use in the same manner.