Sorry, I can't see how different tyres makes (front to rear) would cause such an reaction from the traction control. Accelerating, braking, turning, road surface, tyre pressures...does anyone really think that the load and grip provided by 4 identical tyres would be equal?
If you've got the car on the limit then yes, eventually one tyre will be the first to give but it doesn’t sound like the car is on the limit in this particular case.