Last time Southern was up, didn't it apply only to journeys on Southern? That restriction isn't there now. If the new conditions are a mistake, they better honour them!
Current terms for reference:
"Please note, cashback is paid per completed basket (booking), not per ticket. Cashback is only valid for Anytime, Off Peak and Advance tickets bought via southernrailway.com and excludes weekly, monthly and annual season tickets."
I'm assuming that "Off Peak" here means any of the different types of off-peak tickets, however branded, such as Off-Peak Day, Super Off-Peak, Cheap Day, etc.?