TLDR: Yes, some turbochargers need time to decompress otherwise they could be damaged.
Perhaps my answer only applies to old turbocharged vehicles. My experience has only been with an early 90s Nissan Exa and an early 00s Subaru WRX and both of those had a "turbo timer". With the timer the car would continue to run for about 1 minute after switching off the ignition (and removing the key). My understanding was that this was normal for turbo cars.
Turbos can generate a lot of pressure when it's running. That pressure needs to have somewhere to go. When the engine is running it just blows out the exhaust, but when the engine just stops there is a buildup of pressure (not enough to crack a piston head like I've been told but), enough to blow backwards through the compressor, damaging it.
Here's an excerpt from wikipedia
In this situation, the surge can raise the pressure of the air to a
level that can cause damage. This is because if the pressure rises
high enough, a compressor stall will occur, where the stored
pressurized air decompresses backward across the impeller and out the
inlet. The reverse flow back across the turbocharger causes the
turbine shaft to reduce in speed more quickly than it would naturally,
possibly damaging the turbocharger.
Turbo Lubrication and Excess Wear
The engine feeds lubricant to the turbo. With the engine off the turbocharger isn't being lubricated.
This from turborepair.com:
Once you turn off the engine in your car, the turbocharger will
continue to spin for up to a minute or more and during this time oil
is not being delivered to the turbochargers bearings, causing wear.
This from myturbodiesel.com
If you were driving hard and hot, a 1 minute idling period or a few
minutes of sensible driving before shut down should be enough to let
the turbo cool down and receive fresh oil. If the turbo is too hot
and does not receive cooler oil upon shutdown, the oil could become
burnt and "coking" may occur.
This from allpar.com
Hot shutdowns cause extensive deposits of carbon and shellac on the
turbine end. As the deposits break up and flow into the oil they score
and wear the bearing bore, bearing and shaft journal.
Turbos don't run all the time, they only run when they need to. Which means if you've been coasting around a car-park for a minute, the turbo isn't running and there is no pressure buildup. In this case you don't need the turbo timer, you can shut off your engine without waiting.
You can read about turbos here and here's some rev-heads talking about turbo cooldown and how important it is.
RedGrittyBrick's answer mentions 2 links:
turbotechnics.com (a manufacturer) say allowing the turbo to decompress is "worthwhile" in some instances.
turbobygarrett.com (also a manufacturer) say hotstopping can "result in oil coking". It also says water cooled systems can reduce this, but not all turbos are water cooled.
Many Garrett turbos are water-cooled for enhanced durability