have you turned the TC off
if so TURN IT BACK ON !!
TC only works by detecting slip of either of the rear wheels by speed differential. It doesn't detect nor correct oversteer. If you throw the car into a corner with far too much power on the inside rear wheel will unload and spin straight away and the TC will indeed cut power before an oversteer develops. In fact, in this instance, the spinning inside rear wheel does a good job of limiting the torque to the outside wheel and will probably prevent the whole back end braking away unless you're "doing a clarkson" with the throttle pedal or you have a limited slip diff.
With gentle acceleration and cornering, perhaps on a slippery surface, the back end can get quite wayward without a large speed differential between the two back wheels (since they have both run out of traction - hence the slide) and TC will be none the wiser.
TC also backs off the power rather quickly IMHO, although only with quite a bit of power on in the first place. As mentioned, a rapid lift-off is just as bad has putting too much power on in the first place. Smoothness in your response and not panicking is key. As Hotel21 says, that comes from practicing at Tesco's car park a skid pan.
.. Just don't ever think you can rely on TC to get / keep you out of trouble.
Kevin
Agreed -- it's not stability control, so it doesn't monitor things like the yaw and pitch of the body, nor the steering input. All it will do is try to prevent the rear wheels spinning under power, and it's pretty crude at that IMO. Personally I find it a hindrance and much prefer it off. My right foot serves as a much better traction control device

I think your main problem is the cheapy tyres. I had Kwik Fit specials on mine when I bought it, and it was a nightmare to drive in the wet. I remember coming off a roundabout once and the back end stepped out, I ended up drifting it for about 30 or 40 metres trying to gently bring it back into line, and that was me driving sedately

. It's one thing enjoying controlled drifting at the right time/place, it's quite another having to deal with it every time you apply more than 10% throttle! I done my utmost to wear those tyres out (including copious amounts of donuts in the Knockhill car park

) then replaced them with Michelin Pilots -- much more expensive, but cheaper than writing your car off!
BTW as mentioned by TB and some others, snapping the throttle shut is the instinctive reaction that will be fine at small slide angles and lower speeds, but I wouldn't recommend it if the car gets really out of line. You can then experience lift-off oversteer due to the weight shift, where the fronts suddenly grip much more than the rears, meaning that even though the rears are no longer being asked to grip in anything more than the lateral direction, the momentum and lack of weight can cause the rear to spin round past the point you can catch it. A gentle reduction of power while counter-steering is the best approach, and it should tuck back in nice and smoothly.