cron.weekly day of the week inconsistent between systems

Issue

cron.weekly jobs run on different days of the week for different systems. I.e., when installing RHEL on a system on Wednesday, then cron.weekly runs on that day of the week for that system. The day of the week on which cron.weekly runs varies from system to system. The desired behaviour is to run it on the same day of the week for all systems. The documentation is not clear on what day of the week cron runs for RHEL 6, or how it is controlled.