This is pretty simple to solve for. Eg. Have the app provide an ID the customer can quote to the CS rep; Have the app also log this ID, along with the system it's being run on, to the cloud/an interface that pops up an "unsupported system" message to the CS agent on entering the ID.
I don't see an issue here… He was completely honest about working two jobs at once, to the extent of putting it on his resume.
Surely you'd have followed this up with some questions about how the contracts for those two jobs were worded, or that you'd expect someone to be working full-time for yourselves and wether that would be acceptable?