Science time! That funk motorsports unit is good. Seen them do work on SR20s. I was gonna get one in the near future due to that.
The purpose of a turbo blanket is purely to thermally isolate the turbo more. This does mean, as Grip-addict mention reduce engine bay temps but more importantly it keeps the turbo hot and everything around it cool(even the oil leaving the turbo). The blanket won't
save a car but it counts on these 30 year old things.
The spooling increase is primarily due to retaining a larger amount of heat. The wall of a turbo is really just a big heatsink, and some of the exhaust heat is just absorbed by it. When you blanket the turbo it retains the heat and less of it will be absorbed thus allowing more exhaust to be recycled. This does help but BUT is very slight say, a 200RPM turn in can be seen and a .5ish second decrease to engine 'ramp up'. These are noticeable, especially for a mod that just sits on the turbo, but its not a game changer.
Heat cycling is reduced as well, as the turbos stays hotter longer. This can help with the lifespan if thats of concern.
This video broadens this topic and explains areas and what a turbo blanket effects.