Theoretically, this would be possible, but it would require you to project your coordinates onto a coordinate system which lines up with the map. And that would be very difficult with an image. You might be better off trying to use a different map projection. Sarah Battersby has written a series of blogs which may help with this.

Working with projected data in Tableau – Part I: Map projection basics

Working with projected data in Tableau – Part II: Data manipulation

Working with projected data in Tableau – Part III: Even more data manipulation (inset maps in one worksheet!)

Working with projected data in Tableau - Part IV (base map tiles & polar data...the final frontier)

Yes, I would agree with Ken, unless there is a hard constraint that you must use this image file as your map, I would try another map source.  The data in your file seems to work well with the built-in Tableau maps.  If you must use the image file you've put in the file, as Ken said, try playing around with coordinates to get them to line up -- it may not be possible.  I tried and got the west side of the map to line up but the east wasn't even close.  This is what it looks like with Tableau's built-in maps.  Labels for the Names will pop right on

Do you have coordinates for the DMA boundaries?