It's not the Macs, it's Finder tags are not supported or maintained when using iCloud drive from Safari. This is similar to DropBox. For Macs using iCloud you must drag/drop to/from Finder, not Safari. With DropBox you must drag/drop to/from Finder, not Safari -- otherwise Finder tags are not maintained.
If either computer on either end uses iCloud Drive or DropBox from Safari, the Finder tags are stripped out.
It might seem logical since they are "Finder" tags, but copying the same tagged files to/from DropBox or iCloud Drive using Terminal works -- the tags survive the trip.