Thanks for the feedback.
The initial eBay integration only handles the process up to the point where the item is actually shipped. As soon as it's given to the actual courier (like DHL, UPS, ...), the app adds another status message like "Further tracking information was supplied" including the tracking ID.
If, and only if this message gets added and the courier is not labeled "Unknown", you will receive further tracking information from the app.
From your description, I suspect that your order was shipped with the eBay global shipping program. Unfortunately, this is not part of the API eBay offers for developers and because of that, not supported in the app. Thanks for your understanding!