To manually fulfil 'Product IDs', sign into your AliExpress.com account:

After signing in, go to:
> Account > My Orders

From within this page you can find your 'Order IDs' here:

After locating the correct 'Order ID' for the product, copy it, open your store dashboard in a new tab and go to:
> Orders

From within this page click the 'ID' number of the order you'd like to manually fulfil product IDs in:

Scroll down to the heading 'Products' and paste the 'Ali order ID':

Go back to the AliExpress tab and next to the order click the button labelled 'Track Order' to reveal the 'Tracking ID':
*The 'Track Order' button is only visible once the supplier has shipped the item and has updated the 'Tracking ID' (can take a few days)*

Copy and paste the 'Tracking ID' in its corresponding box:

(*Don't forget to click 'Save order and tracking IDs' after making alterations*)