If your crankshaft turns clockwise, yes the right hand mount will be pulled up and the left mount will be pushed down. But please, please understand that the engine does not turn the other way when the car is in reverse. That happens at the gearbox so your driveshaft will rotate backwards. The engine keeps going one way, all the time.

What direction is force applied to engine mounts? If engines turn the crankshaft clockwise (when facing flywheel) then would the torsional force pull the right hand mount upwards and the left mount downwards?

(When the car is going forwards ..)