The autopilot would not make an aggressive correction. It’s likely that the application of speed brakes along with a downdraft after the updraft caused the injuries. There was no reason to use speed brakes at 37.000 feet. Nothing good would come from it. Airlines in that region often penalize crews for any transgression and the crew may have panicked thinking they would over speed the aircraft. A over speed is preferable to using the speed brakes at altitude trying to maintain level flight.