Afaik, there should be no problem in running multiple instances of (the same or of a different) process.
Based on your description that all process instances are being created using the same process instance id, I can only assume that there must be an issue with the id generation when using mysql? Did you try to run the same test using the h2 as configured in those tests by default? Does that give the same issue?
If you could reproduce the issue, can you show me your code, so I can give it a try?