The only cooling that sort of turbo gets is from the oil flow and just a little from the air flow at idle. The problem is to cool it down enough that the oil in the bearings does not get cooked to tar or charcoal after the turbo shuts down. You are on the right track a couple minutes of low load idle to get the heat out of the scroll so it does not burn the oil, but will have to defer on a specific time recommendation since all my turbos have been water cooled.
The turbo buick guys usually say 30 seconds to a minute or two depending on how hard they were flogging the car before shut down.
Saab used to recommend a minimum 30 second cool down at idle before shut down on the Saab 9000 turbo.
With modern synthetic oils which have higher temperature limits than conventional oils used years ago it probably is less important than it used to be if you are running a premium oil.
You might put an oil temp gauge down stream from the turbo if your configuration allows, but 30 seconds to 2 minutes sounds like a good place to start.
The high power turbo diesel guys might have a better recommendation but that is what I recall on the subject.