The way I understand it...

When a supersonic bullets enters the transonic velocity the pressure instantly and violently shifts from the rear of the bullet to the nose of the bullet. If you look at a back lit photo of super and sub sonic bullets you will see the shock wave shift forward of the bullets nose when it goes subsonic. I believe when this happens it is almost like the bullet hit a solid barrier and thus tumbles.

In the pic below you can see the shock wave shift forward of the bullets nose and instantly the bullets is pushing against real air instead of the shock wave.

Another thing that happens is ultra low drag created during super sonic flight disappears and the bullet instantly feels greater drag which i believe adds to destabilizing the bullet.