Backed out primers is a symptom of low pressure.

The shot cycle works like this.
1 firing pin hits primer and shoves the case as far into the chamber as possible, i.e. as much as the head space allows.
2 primer ignites and the explosion forces the primer out the pocket until it is stopped by the bolt face. The primer flash also sets off the powder.
3 burning powder increases the pressure inside the case and makes the case swell and grip the inside of the chamber walls. Also start forcing the bullet into the barrel.
4 as the pressure inside the case increases, it streches the case body above the web until the case head contacts the bolt face, reseating the primer in the process.

In your case, the pressure did not go over the plastic limit of the brass to stretch the case and reseat the primer.

Good explanation, thank you.

Any idea how the extractor missed the case rim in those two cases ?

All subsequent 24 full-power rounds in the test extracted properly.

I presume the action has a push-feed bolt face.
Judging by the protrusion, those cases were sized to a very generous headspace. Could be that the extractor did not hook the rim when closing on those 2. Or maybe the were jarred loose when the firing pin hit. And, because the case did not stretch, the head never extended back to be hooked. The rims do look quite thick on the photo.

You obviously won't have the problem on normal pressure loads.

 I bought some primed Lapua brass a while back, and used most of them.  I only checked them for length, not the headspace dimension, most of them needed trimming. These three are from the remaining. 

I have a few more, it will be worth measuring the headspace on them, and compare to the headspace of my regular sized brass to see if the difference is that primer protrusion.

@janfred

Spot on. The headspace measurement of both the fired cases with the protruding primer are where my properly sized brass is at : 80.00mm.

The primed brass I bought has headspace measuring  -0.3 to -0.85mm away from 80mm.

Thanks for the input. Eye opening.

I have explained this as, the primer was ejected to early (usually only moves back a bit later in firing sequence - but loose pockets or undersized primer) and then case followed. The early backwards movement caused the the primer to bulge under firing pressure(predecessor to rupture). The case then followed incorrectly timed and riveted the primer a bit due to primer sidewall bulge from pressure

Dave, you just explained why primers are flattened. Due to pressure or excessive headspace.

Also eplains why primers can look fine even at high pressure if the headspace is very small.