Sounds like your DNxHD was exported in 601 / 709 color space (16-235). Pr works in RGB (0-255). You can put a levels filter on the footage, and set the RGB input black to 16, and input white to 235, and that will adjust it for RGB editing.
Yes you're absolutely right. It was a 709 version, and the levels filter makes it look right. One thing I like about Avid is the option to choose color space for each clip during import; is there no equivalent in Premiere? It seems like it would be a hassle to apply this filter to every clip. Almost everything I work with is Rec709.
It is a little odd that Ae accomodates for color space, but Pr doesn't. You can put in a feature request.
You can minimize the hassle by putting the Levels filter on an Adjustment Layer, or you can copy the effect after you've made the 16-235 adjustment, and paste it on all your video clips.
And, if you have control over the exports from Avid, there is an option there to export in RGB.