It's all about physics...A good book "Ayrton Senna's Principles of Race Driving" talks about just that exact problem:

Chapter 3 - Cornering: Controlling the Car
"...The car must never be left decelerating because the speed would magnify the tendency to oversteer: if the car starts to go from the rear end, never lift from the throttle, or there will be a ruinous spin....It is a mistake to lift off the throttle completely and decelerate violently: if this happens you could experience a sudden shift from understeer to oversteer."

-Justin

 

you want to rev-match when shifting while turning. rev-match to match the engine and transmission speeds.

 

You should be shifting BEFORE the turn at the same time that you are braking. Both braking and shifting will tend to shift the weight of the car forward, so you need to do those before you enter the turn. (Of course, you will be braking into the turn as well, but that isn't a problem if you are entering the turn under braking, because you will already be compensating for the weight shift.) As you enter the turn stay on the clutch, and use heal-toe to rev-match the new (downshifted) gear to your current speed. Then release the clutch and break and let her scream!