The difference may be caused by the presence/absence of the color profile in the image file. Do you keep all files in the same file format (for example TIFF)? If the file format is changing then the color profile may be not preserved, so I would check that in the first place.
Thank you, but,...
I always export in tiff format whith ProPhoto RGB color profile, the same file and format to export to Cs6, without changes and nead stand alone whith changes.
Please export the image from LR into a TIFF file and then use that TIFF as a starting point for a test: take that TIFF through two different workflows, one with Neat Image and another without Neat Image, compare the results and describe the workflows step by step. We will need these descriptions to reproduce your results. We will also need that TIFF for a direct test.