The shafts on most turbochargers spin in excess of 50,000 RPM and generate lots of heat. To keep your turbocharger's heat under control, it is cooled by circulating oil or water (coolant) around the shaft. The turbocharger's shaft is free to rotate at will and there is no way to stop the shaft from spinning after shutting the engine off.
To dissipate and stabilze the heat in the turbocharger, most manufacturers recommend that a car be idled for a period of time after moderate to hard driving to allow the oil/water to take heat out of the turbocharger
Though the oil pump, to the turbo, does carry on for a period of time after you shut the engine down.