When the BridgePal app runs for the first time after installation it allocates a "device id", using a random number generator, and writes this to the app's private storage. This device id is included in requests to the PC and is used by the BridgePal software to uniquely identify the device. The fact that this allocation is only performed the first time the app is started means that you can exit the app or reboot the device in the middle of a bridge session and the BridgePal software on the PC will still be able to tell which device has reconnected and restore it to the correct point in the session.
I guess that when you cloned one of your existing phones the Samsung software must have copied the BridgePal app private storage, which would include this device id. Therefore, the BridgePal app would not allocate a new id since one existed already. I'm not sure why the BridgePal app wasn't included in the cloning - perhaps it was originally downloaded and installed from the BridgePal website onto the phone being cloned, not from the Play Store ?
I just tried uninstalling/re-installing the BridgePal app, and that did result in a different device id being allocated, so perhaps it's not necessary to do a factory reset.