Reynolds357,
Sure Shot Mc Gee is employing the less commonly-used meaning of "countersink" which, in addition to cutting a lip recess around a hole, also means to set a nailhead below flush with the surface of a board as with a nail setting punch. The common ammunition maker's terms for doing this with primers are a little less descriptive. They are
reconsolidating the primer and
setting the bridge.
Reconsolidation of the primer comes from the idea the primer was initially
consolidated (the parts assembled into a unit) at the factory. The primer stays in that form until the anvil touches the bottom of the primer pocket. You then push the primer cup in an additional few thousandths (0.003" was found optimal by NOIH), and you are said to have
reconsolidated the primer by that amount.
Setting the bridge is a term that comes from the fact the priming mix bridges the space between the bottom of the primer cup and the inverted tip of the anvil. By reconsolidating, you are setting the thickness of the priming mix bridge between the two to a shorter distance.
There are a number of tools available for doing this. The most precise is the K&M Primer/Gauge tool, which uses its primer seating ram two ways. First, with no primer present, the case is placed in its shell holder and the ram probes the location of the bottom of the primer pocket while simultaneously carrying the individual primer you will be seating on a little platform that drives a dial indicator that you zero when the seating ram finds the bottom of the primer pocket. This subtracts the height of that specific primer from the depth of that specific case's primer pocket. Thus, when you remove the primer from the platform and the case from its holder, place the primer over the ram for seating and return the case to the holder, when you have seated the primer far enough so the feet of its anvil just kiss the bottom of the primer pocket, the gauge reads "0". You then push harder until the dial reads -0.003", and you will have reconsolidated the primer exactly that far.
The rest of the tools I am aware of depend upon your case primer pockets and your primer heights being uniform. The primer seating tool that is part of the Forster Co-ax press has a flat surface that stops against the case head, but it has a 0.005" raised area that pushes the primer that far below flush with the case head. The 21st Century priming too has click adjustable primer depth settings, though the increments are 0.0025", which is a little coarse. The NOIH recommended tolerance was ±0.001". There is a bench tool I've forgotten the name of that does the same thing in 0.002" increments. 0.001" would be ideal. You can shim the case holder on the Sinclair hand priming tool to get a fixed seating depth.
Or, you can ignore all that and just seat your primers hard. I can tell you from using the K&M tool that your thumb is applying some force by the end of a 0.003" reconsolidation. That is why, in 1995, the late Dan Hackett wrote:
"There is some debate about how deeply primers should be seated. I don’t pretend to have all the answers about this, but I have experimented with seating primers to different depths and seeing what happens on the chronograph and target paper, and so far I’ve obtained my best results seating them hard, pushing them in past the point where the anvil can be felt hitting the bottom of the pocket. Doing this, I can almost always get velocity standard deviations of less than 10 feet per second, even with magnum cartridges and long-bodied standards on the ’06 case, and I haven’t been able to accomplish that seating primers to lesser depths."
Dan Hackett
Precision Shooting Reloading Guide, Precision Shooting Inc., Pub. (R.I.P.), Manchester, CT, 1995, p. 271.