If a customer requires a refund, you will need to manage this via Kogan.
The process is outlined in this FAQ: How to issue a refund
If you cancel an order or mark it as refunded in your eCommerce system, the status of the order will also update in Omnivore but it will not process any refunds and it will not update the order within Kogan.
How to mark the order as 'Refunded' in Omnivore
Go to 'Orders' in the left-hand navigation
Find the order and click through to the page which holds all the order information
Click 'Mark as refunded'