You control what is used in the order status. Note that the payment method has it's own settings and controls the status used by that setting. If you have the SAME setting in your payment method when a transaction is successful as the condition in your you download delivery your customer will have access once payment is recorded. You just need to use the same status to get the results you want.
You can set the global default behavior for new orders in the settings menu:
Location: Go to System → Settings → Checkout.
Order Status Setting: Here you will find a setting labeled "Order Status" (usually set to Pending by default). This defines the status assigned when an order is first processed.
Payment Method Overrides: Note that many Payment Methods have their own internal settings. They may automatically set the status to something else (like "Processing" or "Complete") for successfully Authorized and Captured orders, bypassing the global default.
You can set the global default behavior for new orders in the settings menu:
Location: Go to System → Settings → Checkout.
Order Status Setting: Here you will find a setting labeled "Order Status" (usually set to Pending by default). This defines the status assigned when an order is first processed.
Payment Method Overrides: Note that many Payment Methods have their own internal settings. They may automatically set the status to something else (like "Processing" or "Complete") for successfully Authorized and Captured orders, bypassing the global default.
