Immigration offices don't really strike me as the kind of thing you'd find in DF's setting, but you'd still think settlements would have some way of keeping out people they don't want. And the best way of making immigrants know they're unwelcome (besides killing them) is to simply not give them a place in the fortress.
I was thinking that a good way of handling immigration might be to have immigrants tag along with each caravan. They'll hang out with the traders at the depot flashing their X's and it's up to the player to assign them a bedroom, or mark a dormitory to accept immigrants. If they haven't been given a place to stay, then they will leave with the caravan.
So to simplify, a bunch of immigrants will come in with each caravan. The player (ostensibly whichever dwarf is in charge) can:
-Manually assign a bedroom to a specific immigrant. Immigrants would not take empty rooms on their own - only dwarves belonging to the fortress would do that.
-Mark a dormitory to accept immigrants. Dormitories would accept as many immigrants as they have bed spaces. Once an immigrant is part of the fortress, they'll be able to move into an empty room on their own and make room for more. In this way dormitories would act as a kind of 'immigrant buffer.'
There are a bunch of ways to expand on this, but that's pretty much the gist of it.