A JCL job that is scheduled for a specific time, using EXEC CICS START AT HOURS or EXEC CICS START TIME runs immediately instead of at the specified time.

This is actually the expected behavior, as documented by IBM. An absolute time is always relative to the midnight before the current time and may therefore be earlier than the current time. TIME may be in the future or the past relative to the time at which the command is executed. CICS uses the following rules:

If you specify a task to start at any time within the previous six hours, it starts immediately. This happens regardless of whether the previous six hours includes a midnight.