My time capsule appears to also be acting as a router (its not in bridge mode) I know this because the previous network name when the time capsule was the router is still up and running. My question is- is there a problem with this
The fact that the Time Capsule might still be producing a Wi-Fi signal does not necessarily mean that it is acting as a router, although it is possible that it might be.
A lot of users do not understand that the Time Capsule can still produce a Wi-Fi network signal when it is in Bridge Mode.
Have you checked the Network settings in AirPort Utility to verify whether the Time Capsule is set up as a DHCP and NAT router.....or.....whether it is set up in Bridge Mode, which Apple calls "Off (Bridge Mode)".
Do you want to back up using the Xfinity Wi-Fi network.....or.....the Time Capsule Wi-Fi network? If you want to back up using the Xfinity network, then you should turn off the Wi-Fi function on the Time Capsule so that it will act only as a wired hard drive attached to your Xfinity router.
You would also need to have the Time Capsule in Bridge Mode for this type of setup.
I'm not getting a double nat message...
Normally, you would see a Double NAT message if the Time Capsule is set up as a DHCP and NAT router with another router also on the network......unless......you previously chose to "ignore" the Double NAT as an option.
Offhand, I can't think of any good reason to have a Double NAT setup on a network if it can be avoided.....unless you are trying for some kind of special setup to isolate one network from the other.