Your Mac Pro 6,1 ( 2013 ) supports power nap . Maybe this is what is causing this behavior . You can verify whether its active if you go into System Preferences , Energy Saver .
I disable Power Nap on all my machines so it must have been something else. Without a pulsating sleep light you'd never even realise (unless combing through log files is a hobby). So this is why it was removed.
Btw. on the subject of sleep mode: is there a proper hibernate mode in the OS? One that suspends to disk after a while and will continue the session as if nothing had happened even if the power fails? I think I had that going once on a different machine and it was super handy, seem to have lost it in an OS update.
pmset -g
System-wide power settings:
Currently in use:
standby 1
Sleep On Power Button 1
womp 1
autorestart 0
hibernatefile /var/vm/sleepimage
powernap 0
gpuswitch 2
networkoversleep 0
disksleep 0
sleep 0
autopoweroffdelay 28800
hibernatemode 0
autopoweroff 1
ttyskeepawake 1
displaysleep 0
standbydelay 0