By default a mac remote is set to control every Mac in its dance and every Mac is set to respond. But it is possible to pair a specific computer with a specific remote.
Once you do this don’t forget which remote is paired with which computer.
To pair go to
System Preferences > Security.
Select the general tab and use the “Pair” button.
The older (white) remotes are supposedly parable with a Mac by pressing the “Menu” and “Forward” buttons together when close to the Mac (and no other Mac in vicinity).