When I clicked the 'Generate Master Key’ it gave a message box that said: “Success: Master Key Already Exists”. I have a copy of the master key from when I used JB on our old server, so is it the same master key?
Transferring doesn't generate the master key or use the existing master key for the previous server. When Jetbackup is installed, at the install time a master key is generated automatically. You only need to generate a key if the master key is missing. However, all new installations of JetBackup will generate a master key for you.
More details can be found in the below documentation for JetBackup.