The new MOV export option is a great step forwards but its worth noting its not completely featured yet and one of the additions to come is the option to scale the output levels.
Currently every thing exported via the UME MOV is legal levels so no mapping is done.
If you are doing a H.264 export (for playback or web upload)
You may want to add a legal to full levels LUT to an empty upper video track of your sequence before export.