That's interesting, I have 30 WCF and 32 Special rounds with the two piece primers and never gave a thought to them, other than that they were an indication of age.
I doubt your bullets are cupronickel though, for a short period of time bullets were given a tin, I think tin, wash to cut down on fouling. I have a Winchester 32, with 2 piece primer, that has at least half of the wash rubbed off. I'm guessing the adoption of gilding metal ended that process.
Very nice rifle, I'm sure you'll enjoy shooting it, especially with the shotgun butt.
Tim