Why won't my Mac Pro wake from sleep at the scheduled time?
Try resetting the System Management Unit (SMU); the SMU is typically responsible for tracking when your Mac is scheduled to wake up.

With regard to your Mac Pro appearing not to keep time, this is not a problem. It is expected behaviour for the menu bar clock to update a few seconds after your Mac has woken up.

The process controlling the clock needs to get a change in time notification before updating; it will not match your Mac's internal clock immediately upon waking up.