An assembly for an aircraft propulsion system includes a propulsor, an engine, and electrical distribution system, and a controller. The propulsor is configured for rotation about a rotational axis. The engine includes a rotor coupled with the propulsor. The electrical distribution system includes an electric motor. The electric motor is coupled with the propulsor. The electric motor and the rotor are configured to cooperatively control rotation of the propulsor about the rotational axis by applying a total torque to the propulsor. The total torque includes a motor torque of the electric motor and an engine torque of the rotor. The controller is configured to: identify a target rotation speed for the propulsor, identify a deviation of an actual rotation speed of the propulsor from the identified target rotation speed, change a target total torque for the propulsor, control the engine to change an actual engine torque of the rotor to the target total torque, and while controlling the engine to change the actual engine torque of the rotor to the target total torque, identify a torque difference between the actual engine torque and the target total torque and control the electric motor to apply a target motor torque to the propulsor based on the torque difference.