Posterized colors on two different monitors with Mac Mini, late 2014 model

Sometimes when I leave my Mac for a while (like an hour or more), I come back to a black monitor, then click the trackpad to wake it up (I assume it is "sleeping" but I don't see a way to make the monitor sleep), I am faced with posterization of the colors and crumbly text, like this:

I can "fix" it by going into System Preferences > Display and change the rotation to 90 or 180 or something. The screen clears up right away. Then I revert to the normal rotation. This is an ok workaround but it is not convenient. I never had this problem with my MacBook.

I first saw this issue with my late 2014 Mac Mini that I got a couple months ago, and it has happened with both monitors I have tried: an old Benq monitor attached with DVI (DVI to Thunderbolt adapter) and a new Thunderbolt Display. The Benq was connected using a DVI to HDMI adapter. I no longer have this monitor. The Thunderbolt Display is attached directly to the Mini using the Y cable to the Thunderbolt port on the Mini.

Yosemite version is 10.10.2. It doesn't happen if I wake the Mac while it's showing the screen saver.

The only things I have checked under Energy saver is "Wake for network access" and "Enable Power Nap". I don't have anything Scheduled, as I don't have a specific time of day I want it to turn on and off, but I would like the Mac to wake up right way and display correctly if I have to leave the Mac for a while during the day.

I've seen other similar threads, but so far all the suggestions I've seen talking about upgrading to 10.10.2 (which I have) or some sort of workaround involving sleep settings (which I can't quite understand). I'm going to call the Mac Store where I bought the Mini next week, or when I have some time, but I have a feeling they aren't going to be able to help me much. It seems like this is such a common problem with the new Mini's I might be stuck with it, unless someone has a better solution or workaround.