iKeyMonitor does not record websites visited with Private Browsing tab or incognito tab. (Note: URLs typed will still be recorded as keystrokes and websites surfing activity can also be captured in screenshots.) Learn more about iOS Private Browsing.
Besides, it only records websites visited via the default web browser of the target device (either Stock or Chrome for Android; Safari for iOS).
We suggest you find a chance to access the target device, open the web browser of the target device (Stock or Chrome for Android, Safari for iOS) and visit some websites, then open iKeyMonitor to check if they are recorded.