Even with iMessage Apps being so new to iOS 10 I was honestly suprised at how little information there was about the App Store submission process. In particular I had a lot of confusion with the fact that iTunes Connect doesn't seem to treat iMessage Apps as a first class citizen in the App browser. Once I had submitted my binary I struggled for a bit exactly how Apple expected developers to organize their submission, but since I've gotten it figured out I wanted to document so hopefully others can find this informatiopn easier than I could.
First off iMessage Apps are not treated as the app you are submitting. In many ways it is just like a watchOS extension. You create the App in iTunes Connect for your 'container' app, and the Messages App extension is it's own part of that, even if you don't actually have an executable app for outside of iMessage. So your Bundle ID needs to be for your main project, not the message extension. Also, most of the info about your iMessage app still needs to be added in the section for a general app. There are no specific fields for Description, Keywords, etc for an iMessage App. I pretty much filled out all the information as if there was a container app being shipped as well, even though there wasn't. Screenshots as well were required for the container app, and optional for the iMessage component of your app. I was able to just get by submitting the same screenshots in both sections.
All in all it wasn't nearly as hard as it was confusing, and my app was in the store roughly 20 hours after submitting, so whatever Phil is doing seems to be working.