While currently the fix is to simply use NS Site Cloner Pro's options to deselect all the _pm_ tables, this is not applicable for the free version (and is a hassle with Pro). What we consistently see in the logs when trying to process the _pm_ tables is:
At this point the NS Site Cloner goes into a "exit and cleanup" process without actually doing anything. While the foreign key constraint is definitely a keyword, toggling on NS Site Cloner's "Skip Key Constraints" does not resolve the error. I've noticed in the NS Site Cloner changelogs where specific plugins have been catered to in the past. Hopefully the WeDevs Project Manager Pro suite receives this treatment.