I'm not metallurgist but worked with PhD's in our materials lab years ago. I had to refresh my memory but there are basically 3 stages to annealing. First stage (lower temp) reduces what are called dislocations in the grains which create internal stresses. As the temp increases, the unstressed grains can now reorganize which will allow them to grow. If the temp continues to rise, the grains all grow in size. Each of these stages brings a further level of "softening", with the 3rd stage resulting in the softest material.
I tend to think that when we properly anneal cases, we are only taking them thru the 1st stage which relieves the stresses caused by working the metal over and over again.
As for Popper's experience, I'm going to take a few guesses at why he experienced more pressure seating bullets in annealed cases.
Guess #1 - When the cases were annealed, the stresses were relieved, and the necks were no longer as round as they were before annealing.
Guess #2 - Being softer, the annealed cased yielded easier to the bullet, but created a tiny step below the base of the bullet that it now had to push
further down the length of the neck.
Guess #3 - When the necks were annealed the reduced stresses allowed the case diameter to decrease making for a tighter fit.
Guess #4 - If the bullet had a gas check, the softer case neck allowed the harder gas check to engrave the material, causing more drag.