It sounds almost like the ammo was loaded extremely light, as I've had the same thing happen with extremely light handloads.
It could be a headspace issue, but in the rifles I've fooled with that had excessive headspace, the primers usually end up getting slammed back into the pocket and flattened when the case expands and goes back against the bolt head. Of course excessive headspace in conjunction with a fairly mild load might casue what you describe. If it is a headspace problem, it could be the rifle, the ammo, or a combination of the rifle being made to the top of SAAMI specs and the ammo being made to the bottom of SAAMI specs.
I would try a different brand of ammo and see if the same thing happens. If it does, then it's time to start looking at the rifle a bit closer.