When an order is placed for a custom product in your Shopify store you will see that order in the Orders menu.
To process the orders set the status to READY and click the PROCESS ORDERS button.
Processed orders take 1-4 business days to produce. Once the order has shipped the tracking number will automatically be added to the Shopify order in your store.
Assuming you have shipment notifications turned on for your customer, your customer will get their tracking information automatically. For more information on Shopify notifications click here.
Customized will automatically mark the shipped line item in your store as fulfilled upon shipment.
Keep in mind if your customers order is combined with non-custom items (outside of Customized app) you would be responsible for fulfilling those other non-custom items.