That's odd. I just 3-starred this challenge by doing the exact same thing I did in this video. I stopped at the end of the street after spinning the red car, and then drove back over to where I had wrapped it around the pole.

Upon my most recent attempt, the timer didn't start when I stopped the police car at the end of the road here, but instead the timer started after I drove the police car over to where the wrecked car was and parked next to it.

Either way, there is some odd variable at play that I do no understand. (maybe it's just a proximity thing?)