Hi Chwdrhed! FWIW, Here's my opinion.
1- Can anybody prove that it's the same person? I wouldn't think so and therefore I say the other alias whoever it might be has nothing to do with your assistant, even if it him or her, it’s a different site.
2- I try to treat every poster according to how they act on each board. There are a few people I do not get along with and/or have banned on one or more of my boards, but I do not hold that against them on different boards I moderate and visit..
3- IMO the only reason for a dismissal would be if that moderator posts pertinent or personal info from that board or it's moderators on others boards.
In short, No, each board is in it's own way a separate entity in of itself and outside matters should not effect a posters rights or treatment on that specific board.