When you complete C, B, and A class events, you'll unlock the quick tune. You cannot use quick tune in time trial races.
The following cars unlock when you complete the respective class.
S Class - '07 Nissan GT-R Prototype
A Class - '07 Nissan Skyline Coupe Concept
B Class - '07 BMW Concept 1 Series
C Class - '07 Daihatsu OFC-1