The integration should create for each IP Domain that is defined in the PM tool a corresponding Global Collection, that is clearly identified as an IP Domain, with a distinctive green dot.

You need to add the Spectrum device to the corresponding IP Domain that already has discovered the device. The synchronization will take over and fill all the CAPCItemId on Spectrum side, according with the internal device mapping process.
Again, this does not have anything to do with SBGW.