Stop using it and avoid putting weight on the appliance. A hanging disposer that moves unexpectedly needs its mounting and connected pipework assessed before another grinding session.
What the observation tells you
Do not twist it back, tighten visible rings at random or support it with a stack of stored items. Those actions can disturb the assembly or conceal an insecure connection. Keep your head and body out from beneath a suspect mounting.
A useful next step
Photograph the position from the cabinet opening if safe and report whether movement followed sink work, a knock or vibration. Tell the engineer about any leak as well as the movement.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.