In a turbo engine under boost, you may have twice as much fuel mix in the combustion chamber, but since it does not all burn at the same time this additional pressure does not add much to the total cylinder pressure that would have existed in a normally aspirated engine. Now as the piston is accelerating downward there is more burning fuel in the combustion chamber and this burning fuel mix pushes harder than a normally aspirated motor. This is where the real power increase in a turbo takes place. At about 90 degree crank angle the turbo engine's fuel mix is pushing on the piston 3 or 4 times harder than a normally aspirated engine would push. Most of this heat is due to a law of nature that says when you compress something it will get hotter.
Some additional heat is due to inefficiencies in the turbo itself.
What's important to understand is that the hotter intake temperature increases combustion chamber temperature. Detonation can be thought of as a spontaneous explosion in the cylinder, rather than the more desirable even burn. It is for this reason that you must use good quality fuel especially at higher boost pressures and never ever let the engine detonate. Fix the source of the detonation immediately. So you see that while the peak pressure in the cylinder has not doubled, the average pressure pushing on the piston over the entire stroke has doubled.