Crickey... smoking controllers are not good.
Based on this review_ https://www.youtube.com/watch?v=4f30UjuAqZM the Conti set uses what looks like the older "Start" Series controllers.
They have a dial/screw on the side to adjust the tension on the trigger.
First check to see if there is any phsical damage to the controller and that all connections are securely seated.
Inspect any of the electrical connections for tarnishing or burning.
If the set is brand spanking new the controllers sometimes let off a short whiff of smoke from grease/oil and release agents used in the manufacturing process. I had that happen in the past and it never smoked again.
I think the "Extreme" Set has a crossroads/interection piece. If you are using that do double check as some lint/dust can cause shorting there.
If it is damaged or if it smokes again contact the seller or Scalextric directly. The Conti set is fairly new (released end of last year) so they will be interested if there is a quality issue.
The fact that you are using the "Extreme" cars shouldn't make any difference.