The speed at which a primer detonates means that the primer will move back before the base of the case. With a load in the normal range, the primer will move back on detonation, and a fraction of a millisecond later the main charge will ignite, the case expands to grip the walls, the case streches, and the base moves back to press against the bolt face, thus pushing the primer back into the pocket. An excessive charge will cause the primer to be moved back and expand around the chamfer on the primer pocket, but when the base is forced back, the primer, which is now oversized on the "corner" will nevertheless be forced into the pocket, thus creating the flattened primer look that indicates an excessive charge.
But if the primer is not forced back into the pocket, then the base did not move back fully to press against the bolt face. I.e. the case did not stretch sufficiently. However, the neck must have expanded enough to grip the chamber, otherwise the entire case would have moved back, and you might see a lot of soot around the case neck but no protruding primer. Not a simple yes/no answer - there will probably be cases with more or less primer protrusion and more or less soot.
Possible causes: the charge is on the low side and/or the case is too short and/or the chamber is too long! Check the case length before firing for the type of cartridge that has this problem AND the case length after firing of cartridges that performed satisfactorily, where we may assume that, after firing, the case stretched to the maximum length for that chamber. If there is a significant difference (here we need a carbine expert to say how much would be significant - my guess is more than 0.020") then the cases are too short for that chamber. Of course, if you are shooting old surplus ammo, then the powder may have lost a bit of "OOMPH". More than one factor may be involved here.
My experience up to now has been that old surplus ammo can cost more in wasted range time than it is worth. Measure, judge, and act accordingly.