Pressure can indeed be the reason....
But not for the exact reasons given. Consider that both GI and commercial ammo have "industry standard" limits (50,000psi for US GI ammo, and 52,000 for commercial IIRC), and foreign made ammo sould be somewhat close to these specs.
But, the devil is in the details. I do not believe that the difficulties you are encountering are because of the "higher pressure" of the military ammo (in overall terms, it probably isn't higher pressure that what you normally shoot), what is happening is the difference in how your rifle handles the pressure.
Very sooty case necks are a sign of the case not completely sealing to the chamber. This is not a sign of high pressure, it is a sign of (nearly) the opposite. The pressure needed to properly seal the case against the chamber during firing is partially dependant on the hardness (ductility) of the brass casing. "Softer" cases will seal more completely at lower pressures, but at higher pressures (and heat) may tend to "stick" in the chamber, a serious concern when automatic rifles and belt fed weapons are being fed. Therefore, much military ammo, (especially made outside the USA) tends to have harder (or stiffer) brass cases than US commercial ammo.
What is happening is that you are shooting foreign milsurp ammo in your bolt gun, and having smokey necks and a hard bolt lift. What may be a cause of it is the cases not sealing to the chamber as well as the commercial ammo you are used to, allowing some powder gas to flow back around the neck "smoking them", and because of the reduced grip of the case in the chamber, it increases the rearward thrust of the case head against the bolt face. This increased thrust "seats" the locking lugs harder against their mating surfaces, and you feel it as a more difficult bolt handle lift.
I cannot, of course be certain without actual examination of the rifle/ammo, but it seems the most likely explanation to me, based on your description.
A few rounds like this should not damage your rifle, but if you make a regular practice of firing this ammo (case lots) , you ought to have your rifle checked periodically for battering and setback of the locking lugs, or their recesses. Not likely with a modern gun made of modern steels like your Remington, but well known to happen with older bolt guns, especially milsurp rifles converted into other calibers.
It is somewhat ironic that the hardness of the brass, which is intended to provide the best reliability in military auto rifles is causing you some difficulty in your bolt gun, but it is not an unknown situation.
And neither is the reverse, having some military autoloaders choke when fed commercial (or overly soft cased GI ammo). There is a field fix for this problem, which usually works (lightly oil the ammo) but it has its own drawbacks.