Hello,
Well, it's simple F=ma. The thrust is the F, i.e., the force required to accelerate the entire mass of the rocket. Since the mass fell off suddenly, the m changed quickly. However, the control system cannot very the thrust as quickly, therefore, for a short period of time, the F was relatively constant and the m dropped quickly, thus the a, acceleration, increased suddenly. Since the rocket was still in the lower atmosphere where the air is thick, the quick burst may have caused the wind sheer forces to build up tremendously, thus resulting in the break-up and explosion. This is also why I don't think the "destruct command" was ever sent.
Compare this to you pushing a shopping trolley while running as fast as you can. Now, say, something heavy falls off the trolley, suddenly the trolley isn't as heavy anymore. This will cause the trolley to accelerate even more quickly because of the force you are applying, and you will, most probably, fall because you were unprepared for this change in speed.
Of course, this is just my personal view from what I saw on the video. It's very possible I was completely wrong.