You mean: a Steam turbine is being rotated by auxiliary motor when not in operation (No steam running) to keep it balanced.
This operation (if that is your meaning) is not primarily because of differential expansion requirement, but to help keep the Turbine shaft straight and prevent it from bending during stoppage while there is still heat within the turbine and within the shaft etc.
IF THE MOTOR TRIPS, there should be some emergency means of rotating (at very low speed I presume !) the shaft manually or else until safe to leave it. Otherwise, something is missing in your installation or read some more accompanying instructions for this purpose.
To expand a bit on what LAA just said, the turning, or jacking, gear is engaged after shutdown (tripping) to allow the rotor to cool down and maintain it's axial straightness by slowly rotating it; i.e., the shaft will 'sag' and be not be true if allowed to cool down in a static state.
This has nothing to do with differential expansion which is the change in axial length of the rotor due to change in temperature of the rotor.
The turbine cannot be tripped while the turning gear is engaged because the turning gear & motor would have long ago left its place of installment (quite violently) had you put steam to the unit with it engaged. That would have caused an emergency situation!
__________________
In my many years I have come to a conclusion that one useless man is a shame, two is a law firm, and three or more is a congress. - John Adams