Obviously the ship made a turn to starboard before the 13 second mark. Let's say they lost helm with a right 20 order, the ship's rate of turn, as in degrees per minute, is only going to increase as the rudder stays 20° to starboard. It's possible the black smoke you see is the main engine firing back up with an astern propulsion order, which would only increase the rate of turn to stbd. A right handed prop will make the stern walk to port in reverse. There does not look to be anything nefarious going on here. Ships blackout all the time.
Also, the ship would be operating on a marine version of diesel. US ports generally have high quality fuel. I kind of doubt it was a fuel quality issue. I've seen a fuel purifier break and spray water straight into the service tanks. The red MDO looked like a strawberry milkshake, but the engine kept running...