Is Nomie really private?
Yes, Nomie is really private.
Nomie only store your information on your device, not in a server. This is why there are no need for accounts. It's also why you should backup regularly, as you lose your data if you lose your phone.
In fact, Nomie goes a step further than just storing data on your device. Unlike other apps, Nomie doesn't even use tools like Google Analytics or Mix Panel to track app usage. I'm damn serious about this.
How can I test it?
Turn off the internet and you can still use Nomie. The only things that will not work are: Maps, and Time of Day/Day of Week stats. All 3 are rendered from HTML pulled from Nomie.app.
You could also monitor your devices network activity with an external tool.