David,
Are you having PM write out XMP (either as sidecar files or embedded into the RAW file)? If not, you'll need to do that by setting PM to do so in the IPTC/XMP section of the PM Preferences dialog.
You'll also want to cause PM to do the same for writing non-RAW files like JPEGs. And you'll want to make the equivalent changes on the 'Reading' side of that panel. Prefer XMP over IPTC.
Also in the Files section of the PM Preferences dialog set the popup menu labeled 'Add tag, color class, and rating to IPTC/XMP:' to read "For all photos"
These settings will cause PM to put soft edits like tag, rating and color class in metadata that Adobe's software will preserve.
HTH,
-Kirk