BackToMyMac used to run on top of MobileMe but now runs on top of iCloud
Therefore your server (the Mac mini) and your other Macs need to be running at least OS X Lion 10.7.3 or later. They also need to be using the same iCloud account in order to see each other.
I took a different approach, I installed Apple Remote Desktop on the server to administer all the client Macs. This will see local Macs, it will also see remote Macs as long as they are connected some how to the office network including via site-to-site routing or individual VPN connections.
So if an individual laptop user needs help and they are out of the office I get them first to make a VPN connection to the office and I can then see and control them. This approach will still work with older Macs running OS versions that do not work with iCloud.
All my machines are running 10.8.2 and I've done the transfer from MobileMe to iCloud. They all have the same "admin" account etc. and Remote Management enabled. I've also made sure my router has the appropriate ports open. I guess I could use the ARD approach you took. But i prefer to have access to the machine without requiring a user on the other end to take any steps. I've installed LogMeIn as a backup on everything, but it would be nice to stick with the free out of the box tech from Apple