The little dish movers use a couple of relays to reverse the power to the DC motor.
See first picture: two large black rectangular blocks in the lower left are the relays.
Second picture is typical sensor board (yes, two boards in these motors).
Think the black rectangular object beneath the black magnetic cylinder, is the hall effect sensor.
Here's some old propaganda from
STAB, comparing and contrasting their sensors to the then-current competition.
I found it compelling, and bought a STAB HH-90 over the mish-mash of 2100's out there.
Turns out, it was a wise decision at the time.
edit: also, the motors on the traditional screw jack movers for BUDs, and for both the Birdview H-H and AJAK 180 H-H in my signature, are all DC motors with brushes, too