When you tap publish you will see an uploading screen, then a finalizing message and lastly a success message. Once you've see those, your upload is complete. After that:
Your order will be visible under Settings/Order History
You will receive an email confirmation
If the above are true, you’re good to go!
Please keep the app in the foreground while the photos are uploading. Closing the app, or leaving it for another will terminate the upload.