We are applying black power practices (with an external cap, liable to be knocked) to nitro conversions (with a primer surrounded by the metal cylinder walls).
Loading a nitro conversion cylinder is not unlike loading ammunition - the primer goes in first and is protected from damage by the cylinder walls.
I believe that the shotgun primers are a loose fit in the revolver conversions so they may be designed to go in last but on the Patriot pistol, which uses small pistol primers and a special loading press, you most definitely load the primer first.