After installing PrintUsage Pro, I can monitor the print jobs that have been sent from the machine running the management server, but not from network computers.

This is a common problem with using network-attached printers. Network users have 2 methods of connecting to these printers, either via the shared printer that is hosted on the PrintUsage management server, or directly via the IP address of the device. Only by printing via the shared printer will PrintUsage be able to monitor the job information and apply any usage restrictions.