As far as I know, all modern primers use lead styphnate priming compounds which replaced the earlier potassium chlorate which was very corrosive. But there are other ingredients in the priming compound mixtures, and I wonder if some brands might be more prone to cause chamber and bore rusting than others.
Oskar mentions having this problem with Rio and Cheddite primers. I have not had any problem with PB and Winchester 209's. In oskar's earlier thread on this subject, I mentioned using Thompson/Center Bore Butter or Natural Lube 1000 which ended after-rusting problems in my black powder guns. You might want to give that a try. It might stick to the chamber walls better than gun oil.