FWIW, I loaded some .38 Spcl using a hand primer (RCBS) and CCI primers the other day. I noticed that it took a lot more pressure to prime with the CCI than with the Win primers I almost always use (I needed CCI 550 primers for a particular experiment). This tells me the CCI's are ever-so-slightly larger in diameter than other primers. The CCI's also showed a slight indentation where the priming rod pressed hard against them. So it may be that your concern about Dillon/CCI being a bad combo might be true. The Dillon primer may not be able to exert enough force to fully seat the CCI primers.
Can you determine that the primers are fully seated in the pockets? They should, of course, be below the base of the shell by a few thousandths.
Are you getting as deep an indentation in a primer that failed as with a primer that worked? (A shallower dent usually means that some of the hammer force was expended in seating the primer further in the pocket.)
Does a second hammer hit usually fire a round that failed the first time?