How/what sets the Created By User or Last Modified User on the Payment Txn
The Created by User and Last Modified User are set by the Salesforce User that Authorises Payments2Us.
The Last Modified is subsequently set by the Salesforce User that Starts the Batch Processor.
The User the Authorises Payments2Us or Starts the Batch Processor should be a System Administrator.
If you wish to change the user associated with the Created or Last Modified User, then you'll need to re-authorise payments2us and/or stop/start the Batch Processor.