Atlas respects your privacy. Period.
It's pretty simple: Atlas doesn't send any data of its users to its developer (that's me) or any third parties.
What about analytics and crash data?
Performance analytics and crash data could be anonymously collected through Apple's developer platform. You can manage this yourself:
On iOS go to the Settings app and turn on Privacy > Analytics > Share With App Developers. Here's Apple's explanation about it.
On macOS open System Preferences, go to Security & Privacy > Analytics & Improvements and turn on Share With App Developers. See Apple's macOS User Guide for more info.