That's not a domain controller, that's an entirely different domain.
There's not much you can do in this situation if their accounts are allowed to logon to different domains through a trust. This is largely a user education issue.
One thing you can try is leveraging the UPN, which is commonly the same as their email address (user@domain.com). This will prevent them from selecting a domain from the drop down list, and will log them on to the correct domain.