Hello,
Changing the cancellation policy afterwards does not effect the policy related to the specific booking.
Look into your account (transactions and future transactions) to check status of payment for this booking.
Cancellation message's of Airbnb should also provide information.
Refund the guest only via the Airbnb system ("sent or request money"), after proper investigation/monitoring of transactions everything should work out well for you both.
Best regards,
Emiel