So what happens after a primer detonates?

I have first hand knowledge of that event. 40 S&W cartridge with a mis-seated primer detonated in my fingers while trying to remove primer.

Ouch. Never considered one going off that way. I will make it a point to use a decapper instead of my finger nail.
 
When you ask an engineer a question you always get "it depends" for an answer.

The burning powder increases its volume. This creates a pressure. Pressure is force distributed over an area. This force accelerates the bullet.so ultimately the pressure is determined by the acceleration of the bullet. Which determines muzzle velocity. If the bullet doesn't accelerate fast enough something else accelerates
Maximum pressure occurs at maximum acceleration, which could happen anywhere in the bullets path.
 

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