How does the subscription recurring process on the side of Authorize.Net look like?
The Subscriptions And Recurring Payments extensions works with the Authorize.Net payment gateway via CIM service.
When a subscription product is purchased, the extension initiates creating a CIM profile for a customer on the Authorize.Net side. Customer's billing details are stored in the CIM profile only, they are not saved anywhere in your Magento.
The extension checks the subscriptions after each cronjob execution till the moment of the next payment. When the time of the next payment comes, a new transaction is initiated on the Authorize.Net server using the data that is stored in the Authorize.Net Customer Information Manager and then a new order is generated.
What happens if a subscription if a payment isn’t processed on the side of Authorize.net for some reason?
If the transaction fails for some reason ( for example, due to card expiration or insufficient funds ), the order is cancelled by the Subscriptions and Recurring Payments extension and the status of this subscription changes into "Suspended". After that, it should be activated either by administrator or customer again. Then the subscription will proceed to recur if the payment is charged successfully.
Does the Subscriptions and Recurring Payments extension use the Authorize.net Automated Recurring Billing tool?
No, the 1.X branch of the extension only works with Authorize.Net payments via CIM. The Authorize.Net ARB service is not supported.