Customers can't track their packages
In order to allow the tracking code to be sent to Shopify, you need to ship ( PROCESS button) your orders in the back office of the application and not from Shopify
By default, Shopify does not include the tracking number in the emails sent to customers to confirm shipping. So it's up to you (or your developer) to modify the emails so that the tracking appears directly in the Shopify transactional email.