Why aren't tracking numbers updating on orders?

To make sure your tracking numbers post to your orders correctly, ensure that you are not automatically fulfilling the order's line items.

To do this go to your Shopify admin checkout settings (/admin/settings/checkout)

Under Order processing section go to the "After an order has been paid" area.

Make sure you have selected either "Automatically fulfill only the gift cards of the order" or "Do not automatically fulfill any of the order's line items"