If your customer claims to have completed their order via Apple Pay, but you can't see their order, they did not finalize the order, and the payment has not gone through. They did successfully select their payment method (i.e. clicked the side button of their device), but the payment and order will only be processed once your customer presses the BUY NOW button.
Ask your customer to return to their cart in order to complete their order. Your customer needs to click the BUY NOW button on the page following their Apple Pay authorization:
The order has been completed once a green success alert appears on the next page: