While we still have the luxury of speculation, the following video makes some interesting points.
The video is painful to watch, you'll see why if you do, so I'll summarize the mail points.
Ships do have an emergency/auxiliary generator located in a separate compartment isolated from the engine room. Why? Because it powers the engine room fire fighting pumps. It also supplies electrical power for steering.
The propeller of a ship turns in a clockwise direction when viewed from the rear of the ship looking forward. As well as driving the ship forward there is a "paddle wheel" effect which pulls the stern to starboard and thus the bow to port.
When the ship is going astern the effect is reversed, the stern is pulled to port and the bow to starboard.
In the video of the incident, second video, approximately 4 seconds after electrical power is restored following the first power outage thick black smoke is seen coming from the exhaust. Speculation from the first video is that the ship was put into full reverse which would swing the bow to starboard which is what videos of the incident show.
https://www.youtube.com/watch?v=BEzDh4RwpaM (This video can't be embedded)