I believe the NPCs of your alts would have to cosmetic only. Otherwise just having alts would give you an advantage over other players. It would likely also have to be server/faction specific.
I could see it as, whichever character you are playing acts as the owner of the garrison. So if you send followers on a mission on your mage and log into your priest, the followers will still be on the mission you assigned them to on your mage. It could be like all of your characters decide how to run your garrison as a team.