iMac doesn't wake from sleep via USB devices
I'm using Mac Mini with Apple Thunderbolt display. I'm currently in OS X El Capitan 10.11.6. My parameters are the following:

Active Profiles:
AC Power               -1*

Currently in use:
standby                 0
Sleep On Power Button   1
womp                    0
autorestart             0
hibernatefile           /var/vm/sleepimage
powernap                0
networkoversleep        0
disksleep               0
sleep                   0 (sleep prevented by iTunes, coreaudiod)
autopoweroffdelay       14400
hibernatemode           0
autopoweroff            1
ttyskeepawake           1
displaysleep            0
standbydelay            4200


I recommend you to set up all you Energy Saver parameters like this:



And you can put your display to sleep via Mission Control–Hot Corners: