This article covers how the Atlas Recall companion app for your iPhone works, and answers the question of why it doesn't show you results from the iPhone.
Currently, the Atlas Recall app for iPhone is designed as a companion app, which lets you search through your personal searchable library built from your computers (that have Atlas Recall installed).
Any content viewed through your iPhone (other apps, web browsing, etc.) will not be added to your Atlas Recall content.
To read more about how to use or download the companion app, view Atlas Recall on your iPhone.