Recalibrate the compass.
Also, for the compass to function properly make sure Location Services is ON in the iOS Privacy settings. On that same screen, see if you can scroll to the bottom and select "System Services". I believe you need to have "Compass Calibration" ON in that screen. Possibly "Motion Calibration and Distance" as well.
One user resolved this issue by deactivating and reactivating location services!
iOS devices generally do not have issues with the compass mode in SkySafari.