Are the results of Apple Photos processing shared between my computers?
No. In general, all photo library generated metadata is not strictly shared from iCloud to iCloud on macOS Mojave 10.14 and iOS 12 but some of the overall categories / extracted data does sync. (So it’s pretty confusing / grey area at the moment)

Most of the AI training models to identify photos by subject, finding faces, making memories run locally on each device and only after you name a face, save or customize a memory or make an album does that higher level data sync.  

You might need to erase the long running library and let it redownload or better, engage apple support for iCloud and give the engineers permission to look at the sync logs server side and submit some local diagnostics if the process can’t catch up. 

I’ve don’t that in the past to get excellent support and a precise fix. Sometimes the algorithm gets stuck and you need an assist rather than just restarting the OS or downloading a clean copy from iCloud to one Mac (assuming that Mac isn’t your “source of truth” or master copy of photos for you).