Clearly air is being pushed from the main bath into the master bath when
this happens.
If I briefly turn on the master bath's fan and shut it off I can observe it
switch direction after it stops turning in the normal direction.

In other words, if just the main bath's fan is currently turned on, I can
actually see the blades of the master bath's fan spin as the result of air
being pushed from the main bath's fan through the master bath's idle fan.
If I then briefly turn on the master bath's fan for 5 seconds, the motor of
the master bath's fan will wind down after being shut off, but then the
blades will start spinning in the opposite direction since the main bath's
fan is exhausting air in the direction of the master bath's fan.

J.