Install Ring Pro on Rear Doorbell Connection

I have a Ring Pro for my front door and it work great. Now I want to install another Ring Pro for my rear door. I have a Ring Transformer installed along with the Ring Power Kit at the existing doorbell. I replaced the rear doorbell pushbutton with the Ring Pro by only replacing the existing doorbell pushbutton. I made no changes to the connections on my existing doorbell. The rear Ring Pro works successfully. However, now I hear a constant low volume tone from the existing doorbell. I have Trans, Front and Rear wires/terminals at the doorbell. The old rear pushbutton worked successfully on the 2nd tone of the doorbell. I feel something needs to be changed. The Power Kit is only on the front door Ring. I have a "blue" wire that is only connected to the Rear terminal on the doorbell. Do I need to move this to the Front terminal at the doorbell? Any other ideas? Thanks