We present an analysis of stellar populations in passive galaxies in seven massive X-ray clusters at z=0.19-0.89. Based on absorption-line strengths measured from our high signal-to-noise spectra, the data support primarily passive evolution of the galaxies. We use the scaling relations between velocity dispersions and the absorption-line strengths to determine representative mean line strengths for the clusters. From the age determinations based on the line strengths (and stellar population models), we find a formation redshift of z_form_=1.96_-0.19_^+0.24^. Based on line strength measurements from high signal-to-noise composite spectra of our data, we establish the relations between velocity dispersions, ages, metallicities [M/H], and abundance ratios [{alpha}/Fe] as a function of redshift. The [M/H]-velocity dispersion and [{alpha}/Fe]-velocity dispersion relations are steep and tight. The age-velocity dispersion relation is flat, with zero-point changes reflecting passive evolution. The scatter in all three parameters is within 0.08-0.15 dex at fixed velocity dispersions, indicating a large degree of synchronization in the evolution of the galaxies. We find an indication of cluster-to-cluster differences in metallicities and abundance ratios. However, variations in stellar populations with the cluster environment can only account for a very small fraction of the intrinsic scatter in the scaling relations. Thus, within these very massive clusters, the main driver of the properties of the stellar populations in passive galaxies appears to be the galaxy velocity dispersion.