Have you checked the head space? That would be the first thing to do. 7.62 head spaces a few thousandth different than .308, be sure and use the correct gauges for your chamber.
Again he has a .308 chamber not a 7.62X51. He was using the correct ammunition for the rifle. If other brands of .308 ammunition functioned correctly in his rifle I doubt it is a headspace issue. I still beleive it is a ammunition problem, he might have had under charged or over charged powder loads, or oversized primer pockets.
The bullets ogive might have been engaging the lands like one poster suggested which can jump the pressure up as well and cause some of these problems. Unfortunately the OP shot up all the ammunition so he can't put a caliper to it and measure it against the other Federal ammunition he shot as well. He can however compare his fired cases with a caliper to see if they measure any different.
His best bet would have been to stop shooting the Winchester ammo as soon as a primer blew and ship back the unfired ammunition to Winchester to find out what the problem was. I would still contact Winchester and see if they want the fired cases back to inspect. Who knows they might have had a bad run of ammunition that they need to recall.