We study the slope, intercept, and scatter of the color-magnitude and color-mass relations for a sample of ten infrared red-sequence-selected clusters at z ~ 1. The quiescent galaxies in these clusters formed the bulk of their stars above z ~ 3 with an age spread {Delta}t ~ 1 Gyr. We compare UVJ color-color and spectroscopic-based galaxy selection techniques, and find a 15% difference in the galaxy populations classified as quiescent by these methods. We compare the color-magnitude relations from our red-sequence selected sample with X-ray- and photometric- redshift-selected cluster samples of similar mass and redshift. Within uncertainties, we are unable to detect any difference in the ages and star formation histories of quiescent cluster members in clusters selected by different methods, suggesting that the dominant quenching mechanism is insensitive to cluster baryon partitioning at z ~ 1.