Thank you, everyone, for your replies.
It's good to know that cases are in no way damaged. However, it seems the only advantage of using a rotary tumbler, water, Lemi-Shine, Dawn, and pins, over my current vibratory tumbler, corncob media, and Nu-Finish car polish is shiny case interiors. Now, I have to decide if shiny case interiors is worth the extra effort of draining, separating the pins from the brass, and drying the brass, versus just removing brass from the tumbler.