The username@machinename construct displayed in msvsmon is the text that needs to go into the Qualifier box in Visual Studio -> Attach to Process.
For example, where msvsmon says:
msvsmon started a new server named 'tf@macmini'. Waiting for new connections.
you would type tf@macmini into the qualifier box.
For a machine out on the internet, I'd guess you use username@[ip address here], e.g.
tf@123.234.32.1
Though you will need to make sure, at a minimum, firewalls and authentication are set up correctly. (The debugging will not occur via RDP.) There's an article on the firewall side of this here. Can't remember off the top what the authentication involves, although I suspect as a minimum you will need an account on both machines with the same username and password.