How to see lap time records on the screen for non-default cars

Basically, whenever you download some new car from inside of the game, files of that car go to ...cars/tmp folder. To be able to select that car from inside of the game menu, you need to move its files to "cars" folder where all the default cars are. Once you do that, you will also be able to see lap time records of that car on the screen while you're playing some track.
The "tmp" folder exists just as a place where all the cars that we don't care about are. That's the way of how the game doesn't bother you with all the lap times info for the cars that you've, maybe, downloaded accidentally while joining some server.