[JWait]

The customer should get an email informing them that the order was placed. This usually includes the original "invoice" (the pretty one in html... skin1/mail/html/order_invoice.tpl).

Then, depending on the order status they will get another email (i.e. "processed", "declined", etc.). If you want to notify the customer that the order has been processed there is a checkbox for this in the "Email notifications options" section in admin.

It sounds like you are using a payment gateway, and it is possible that they are sending the "processed" email once the credit card is approved. Without knowing how you are set up it is difficult to tell what is happening.

Do you have any additional x-cart modules installed?