normal
the turbocharger shaft, compressor and turbine wheels are all connected together, and at idle speed that shaft assembly with the two wheels is turning about 50,000 rpm. It has inertia. When you turn the engine off the inertia of the assembly keeps it spinning for a bit until it finally stops
most people don't hear it but it is audible if you listen for it
if it's kinda loud and unmistakeable, possibility exists for an exhaust or intake tubing leak, and for those I would look closely at the intake hoses for sure, as well as the little discharge hose that runs from the turbo to the intake manifold, seen a couple of those develop cracks and the usual complaint is abnormal noise. Look at the hoses closely from the turbocharger compressor inlet all the way to the air filter, and make sure everything's properly seated and all clamps are tight, and the air filter is in good condition. Beyond any leaks, without hearing it in person I couldnt' say whether the turbocharger is beginning to die or not, but that would be extremely rare...UNLESS it's ingested dirt or other foreign matter, OR it's lacking (or has lacked in the past) good clean pressurized oil. Generally when a turbo fails, it's obvious. One thing I usually do if it's even suspect is to pull the hose off of the compressor inlet and look inside at the compressor wheel with a flashlight. If the tips of the blades are worn off or otherwise damaged, a replacement is likely in order--and that may not solve the owner's problems, as generally if dust gets in there, the engine is also dusted and may or may not last long
both of my cars and my truck are all turbocharged, the little 4 cylinder in the car has 3" exhaust with no catalytic converter, and a really loud turbine side of the turbo so you can hear it a mile away (not by choice--it's just normal for that turbo), shut it off at idle and it's spinning up to 20 seconds after the engine is off (and audible). THe truck will keep spinning up to a minute, but you have to listen close to hear it (7.3, stock exhaust). Turbo's quite a bit bigger'n the one on the car which is tiny in comparison