the use of the AJAX Remote over the Internet is generally supported. 
Whether it's WiFi, DSL or Cable - it's all TCP/IP in the end and 
Remote Buddy makes no difference between any of these.

The reach of Bonjour addresses is limited to just your local network. 
If you want to connect from outside, you need to make sure:

1) Your Internet router (if any) forwards port 8888 to your Mac.

2) Your Mac's Firewall (find it in System Preferences > Sharing) has 
port 8888 open for connections from the Internet.

3) You access Remote Buddy using your Internet IP. This IP will be 
displayed in Remote Buddy if you have a direct connection to the 
Internet. It will not be possible to display it when you use some sort 
of router inbetween. The IP is only known to your router then. You can 
use services such as DynDNS, though, to get a free domain name for 
your dynamic IP.

Best regards, 
Felix