I do not have much experience with turbo airplane engines but I have a good amount with turbo car engines. In a car if you are in a high load/low rpm situation the engine will bog down and shutter if you try and go full throttle all at once. In a car this is partially due to the load of the transmission. I would assume that the same sort of load is placed on the engine when going full throttle by the prop changing pitch and taking a bigger bite out of the air.
One draw back of a turbo engine is they tend to be higher compression compared to a naturally aspirated engine. This decreases their low end torque in favor of high end horsepower. If you Compare a Supra Dyno sheet to a Mustang GT dyno sheet you can see the difference.
Supra
Mustang
The mustang has almost peak torque from a very low RPM. The Supra needs to wait for the turbo to spool to get the torque you are asking for. The shuttering you feel is the engine struggling to spin the props.
You can stop the shuttering and actually get the power you want sooner by adding throttle in slightly slower but steady pace rather than all at once. When you go full throttle it causes the engine to fight itself. It is dumping fuel in thinking it is getting more air, which actually cools the charge going through the hot side of the turbo. Since turbos rely on the expansion of hot gases you are reducing its efficiency which takes the turbo longer to spool which makes you wait longer for the power you want.