As far as I know (have not tested to verify), if you do not log in to Computers and contacts on the "other" machines, then it will not pop up on those machines. But you will need to make sure you don't have those machines set to auto log on.
So, in your example, if you used the account "Christie" to install and log into the full version of TV on all 4 computers, and all 4 are online, if you connect from Comp1 and try to message Comp2, if TV is automatecally signed in with "Christie" on Comp3 and Comp4 would get the message as well.
In my environment we use "Host" mode installs for most the clients, and only those of us who are goign to be initiating a remote session have the full version. So the Host users only can be controlled, they can't controll another computer. Therefore, there is no account to sign in and you don't have the Computers and COntacts list.
In your case, if you always work from Comp1, then Comp1 could have the full version and Comp2-4 would have host only.