When I tap the radar to switch modes, no matter which mode I am in, If I turn around in a circle, the arrow always points in the Phantom's facing direction.
I suspect it is always using your phone's compass and the Phantom's compass in combination to tell you the direction the Phantom is facing no matter which mode you are in.
Switching modes, as I understand it, changes the center location of the radar between the home position and your phones current GPS location.
I'm testing this without flying at the moment so my location and the Phantom's location are not far enough apart to make a difference.
However, if the phantom is stationary and I spin around in a circle, the arrow spins with me to always face the same direction the Phantom's nose is facing.
If my phone is stationary and I spin the Phantom in a circle, the arrow on the radar spins to show the Phantom's facing direction.
As far as I can tell it doesn't change when changing modes.
All that should change is the position of the red arrow relative to the center of the radar. The direction and distance of the Phantom itself.
FWIW, I'm using an iPhone 5S with location services enabled for the DJI Vision app.