Border of Marching Ants Visible As Part of White Design, After Inverting My Mask

Not sure what I'm doing wrong, any advice would be most appreciated! I have a black and white vector I created in Illustrator and was trying to create two different transparent files of this design, using Photoshop: one that is only the white parts and one with only the black parts. However, the white version is showing a thin line of (static) marching ants after inverting the mask, as if they are part of the design. This might be happening on the black version too, but can't tell with it being black on black, and don't really care. 

What I did: Exported my ai file as transparent PNG > place embedded transparent (no background) black and white PNG and converted it to a Smart Object > Select > Color Range > left click to sample black (Color Range settings: Fuzziness- 95%/ "Selection" checked/ Selection Preview-none) > clicked OK > marching ants appear around my selection > clicked on mask at the bottom of layers panel > command i, to invert.

And, as stated above, the result is all the white of my design but with a really thin border of static marching ants outlining every white shape. Will this border appear after exporting? And if so, how do i get rid of it?

Thanks for any advice!