Hi @movinggifts, I believe the parts of Expo you’ve asked about will work for your use cases.
With Expo you (the developer) own your own code and data. The sentence you quoted from the terms refers to the Expo client application (which you use to develop), which is open sourced here: https://github.com/expo/expo.
You still own the code and data for your own application made with Expo. We should probably clearly distinguish between “the Expo application” and “applications made with Expo” in our terms.
One way to think of these terms is like GitHub: they own their website’s code and databases but you still own your own code and data that you push to origin.
@adamjnav’s solution is correct (as of summer 2017). Setting
"privacy": "unlisted" will make it so that your Expo project is not indexed.
We find that some big projects choose to be listed publicly because it’s easy for people to try them out but that choice is yours. Either way, you still own your code.