I think what Andy is referring to is the spool down time for the turbo be it petrol or diesel,the turbo can be spinning at many thousands of rpm after a burst of acceleration and there is a risk that a sudden engine stop can leave the turbo still spinning without oil being pumped around the bearings
Yes, and, in addition, the turbo will be
very much hotter than any other part of the engine to which the oil circulates. Shut it down at this temperature and the residual oil in the bearing might get hot enough to scorch, leaving deposits on the bearing which will result in its' untimely demise. Leave it idling and it will continue to be cooled by the oil.
Probably only needs to be 30 seconds or so without load but, in a scenario where it comes from towing a caravan on a motorway, into a service station and engine off.. might be good practice to let it idle a little.
Some turbo cars have a water cooled turbo with either a thermo syphon or an electric pump that runs after the engine, but many have only an oil supply, which doesn't allow any flow after shutdown.
It goes without saying that petrol or diseasel is irrelevant, as the turbo is pretty much identical.