I haven't tried an UltraStik with joy.cpl before. I always use gamepad-tester.
Anyway, I get the same results you do with joy.cpl. That ultrastik should work fine with the quadstick or QMP.
In QMP, turn on Enable CronusMax PCPROG:
Restart QMP if the UltraStik was not plugged in prior to launch. You should see:
Version: 3.09.2
QuadStick drive letter: H:
Loaded preferences OK
QuadStick Game Controller interface successfully opened
UltraStik 360 Joystick 1 interface successfully opened
The External Pointers tab should show the crosshairs moving.
Do not make any configuration changes to the UltraStik with UltraMap. The Quadstick and QMP expect it to be in its factory default settings.