Ok that makes sense i think...
You have one screen running at 1080i and the other at 1080p. I suspect what is going on it that when you run videos full screen the players (or probably the underlying Mac OS display components) attempt to put the displays into Vsync mode to avoid their being tearing on the output. However as one of your screens is interlaced it is effectively running at half the framerate of the other screen (or possibly half the vertical resolution, i'm not completely sure how this works in OSX) either way you have a mismatch and this results in the corruption that you're seeing. Its possible that this would even happen with both screens running in 1080i as the outputs are not framelocked and so there is the possibility of a timing error fault.
My primary suggestion would be to avoid using clone mode. There are a number of different ways you can do this whilst maintaining the preview for your operator. The best solution is to switch to using a better playback software, there is a massive range of playback software for OSX which is designed for live shows and or broadcast playout. If you have some budget to solve this then I would look to
OnTheAir VideoExpress or
Playback Pro or
QLab or
ProPresenterAll of these can be configured to give an onscreen preview and control interface whilst outputting fullscreen video, they are all designed for the task and work well.
If you have no budget then it is possible (if a little tricky) to get VLC to show controls and a small video window on one screen and fullscreen video on the other. I've done it once or twice but i don't really remember what combination of settings i used.
The other option which works quite well if you really *need* the clone type setup is to connect the main output to your ATEM, and send a signal back from the ATEM Aux output for your operator monitor - select the Mac input on the AUX and your operator will always have a preview. This works well (i've done this with rMBPs when we have needed to send both output and presenter screens from keynote via the ATEM, whilst having a local operators monitor. There is a small latency on mouse movements but you get used to it very quickly)
Hopefully one of these ideas will work for you, please let us know what you end up doing
cheers
tom