There are two options for using the WP eStore's manual checkout with the WP Affiliate Platform plugin.
Option 1: Under the "Payment Gateway Settings" tab in the settings menu of the eStore for "Manual Payment" option you can check the "Automatically Award Affiliate Commission" checkbox. When checked the affiliate commission will be automatically awarded to the appropriate affiliate after the manual checkout submission. If the customer does not send the payment then you can delete this commission from the "Sales Menu" of the affiliate plugin. You can also add in a negative commission equal to the original amount to show that the commission was reversed (since the payment didn't go through).
Option 2: If you do not check the automatic commission awarding checkbox, you can manually add the affiliate's commission in the Affiliate platform after you have received the payment.