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Based on attached image, the Non Overlap DriveTime tool appears to be working, There's a border created where the two polygons would normally begin overlapping at the top part of the image.
That being said, if you'd like to fill and distribute the area between those objects there are other spatial tools in Alteryx that can accomplish that. The two drivetime polygons shown can be combined and processed to give us the "hole" object. Turn this hole object into grids and distribute them to the nearest polygon, then combine those objects with the originals.
Oh I didn't realize there was that much overlapping area. You're correct that the area should be redistributed like my example. The Non Overlap Drivetime tool is actually a macro that can be opened and debugged to see where the problem is. I could help with this if you'd like to share information on your input points, drivetime distance, and guzzler vintage.