Should I Fulfill The Order Manually Inside Shopify?

The answer is NO.

If you fulfilled the order manually inside your Shopify store prior Zero Up™ fulfill the order, Zero Up™ will not be able to tell that the order was never fulfilled since it is already being marked as fulfilled in your Shopify store.  Once your vendor has update the tracking number on AliExpress, Zero Up™ will automatically fulfill your order with the tracking ID. Then, your order will automatically be marked as "Fulfilled" inside Shopify.

If you fulfilled the order before Zero Up™ fulfills your order, you may need to use the "Track via Extension" button to retrieve the tracking id again.