Your customers table will need to hold more than an id and credit values, you will need to have a way to associate this info with the customer when they return to the site. You should have a full customer registration and login system in place to accommodate this.
To get this update to occur you will do this on the checkout success page. When the user completes the transaction they will be sent to this page. On this page you ensure that the transaction happened correctly with the code that is already on the page.
You will first want to have a recordset on the page to check the current credit value for that customer. You would then just add in an update server behavior to update your users table and add to the credit column.