USCA tech question - tire tread depth?

[Panteracer]

Just got new fronts for my car--Falkins
wondering how they will work with a different
type and age tire for the rear.. autocross, stop box
I think ok.. but track??? Viper guy I track with a lot together and
has found when he puts new tires on front and leaves
his rears the car has a shake or thunking noise....
Well that is what he says after that Black Pantera goes
past him

Bob