What physics is behind the slowing down the main engine for turbocharger water-washing?
Injected water droplets slow down the turbocharger rotor and thus it's capacity will be suddenly reduced, less air will be supplied to the engine. This may lead to surging and subsequent damage to the blades or bearings.
The engine needs to be slown down in order to reduce the scavenging air demand so the drop in the airflow through the turbocharger is minimized. This helps to prevent surging and reduces mechanical stress.