The case material shouldn't (according to the makers) have anything to do with extraction or feeding. But it does, sometimes. I would bet that the Taurus owner's manual tells you somewhere in there to use quality ammunition, so I would spend a buck or 2 more for brass.
It's been a long while since I owned a .380 auto, but when I did, it frequently failed to eject. One of the things I did to remedy the problem was to check my grip to be certain that I was not limp-wristing the thing. Sure enough, that's what cleared it up for me. That sharp, snappy recoil on those little beggars can reveal minor defects in grip and follow through very quickly. Just one thing to consider.