The game records your winning streak and Kart Pro completion status when it finishes saving a race's result after it ends.
Note: It does not record that information the moment the race ends, even if your position and completion status is displayed.
There are times when a winning streak is not properly recorded if the app is shut down in the time before the results are saved, or if a communication error occurs.
If a communication error occurs, please also see the article entitled "A communication error causes me to disconnect during a race."