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You're thinking far too macro to grasp a fundamental basic concept of what makes a turbine go around in a circle.

Forget your test for a minute. Think about just the turbine. You can spin it with your finger or with a drill or with a water hose or leaf blower... SOME force has to move it. In our case were using gasses. Other than adiabatic efficiency and thermal stresses/damage, we really don't care about the temperature.

An oxy/acetylene torch burns upwards of 4500 degrees F. If I apply a 4500 degree flame to the vanes of a 171702 borg warner, It won't spin the turbo at 100k or so RPM. It will just burn the vane.

So getting back to your example...let's cover some basics first.
WHY do we use fuel in an internal combustion engine? To produce heat, sure...but WHY are we producing heat? The reason is to expand gas(not gasoline...air). The expanding gas is what drives a piston downward. Not the heat. The gas is only expanding because it was heated.

This will blow your mind: Pistons can also be moved by gases contracting. Liquid nitrogen (which is around 321 below zero F)used as a fuel can contract gases in a cylinder and draw a piston upwards.

A turbocharger is made up of two completely separate turbines joined together by a shaft. One turbine provides rotational force to spin the other turbine which compresses air. (This may be where youre getting tripped up)The only real difference between this arrangement and a blower is that a blower is rotated by a belt connected to a crankshaft. The only difference between water providing the force and gases is...well, ones a liquid and ones a gas.

The reason that you "see" more boost at a set pedal position at the same RPM is because you're only "seeing" a very small piece of the picture. If you fail to grasp these fundamental concepts, you'll never fully understand how to extract efficiency.

 

I didn't put any words in your mouth. That was my very own example to try to explain the dividing line of what's going on between volume and pressure of gases and heat. Your example was really just posted out of place and was not relevant to the conversation about exhaust.