I've experienced that when I had an M14 - the last shot of the magazine that resulted in the bolt being held back always resulted in a weird vibration.
Every gun vibrates when you fire it but most of the time you wouldn't feel it. Barrel tuners attempt to reduce the vibration at the muzzle to zero (make it a "node"). Sometimes muzzle breaks and silencers/moderators will improve accuracy for the same reason - the extra mass and position of it will reduce the muzzle vibrations. Sometimes they don't change the accuracy but the point of impact, once again because of the effect they have on the vibration at the muzzle. Some rifles can also be affected (accuracy, point of impact) by removing the front sight.
If you can feel the vibration through the stock I would say that is a good thing and that the action screws are tight. Loose screws would tend to dampen the vibration coming back through the stock.
