Order pending but credit card charged drupal commerce
The answer is you need to set the workflow to set the order as completed. Commerce out of the box takes the safe route and assumes nothing about your shopping cart workflow. There is an email that can be configured in Rules for the order confirmation.

The order confirmation email is sent by the rule named Send an order notification e-mail that is under the tag Commerce Checkout in the Rules UI.

To update the order as completed you will need to create a new rule to set the order as completed based on your business rules. It can be as simple as setting the order as completed upon successful completion of an order.

You can use the event Completing the checkout process which will trigger after a successful card charge with Auth.net module or any of the other payment modules, Conditions are none for a simple checkout, actions are Update the order state, data selector is commerce-order then "Order State" is "Completed". 

Here is a visual of the rule: