I would put in that a night kill, by the vigilante, should be secret; ie: the hunter was hidden and couldn't be seen.
Just like we can't see who the wolves are, when they make a kill.
Actually this is what I would do, I said so in the opening rules too. Typically the village wouldn't know which was the wolves kill and which was the vigilante kill.
But because billy was killed the same night, everyone knew which kill was which, so that's why I just said the vigilante killed mott, rather than leaving it general and ambiguous.