For a given lens/camera, all images taken with or without any filters will need WB correction to account for the varying shooting conditions. Even when no filters are involved, one can't use the same WB settings for an image taken in 2700K light that one would use for the same scene taken under 6400K light and expect the colors of the objects in the scene to look remotely similar.

And here is another RAW file, shot with my 6-stop ND filter. Same tripod, same composition, same lighting (different exposure settings though). Also used auto-WB. Resulting in temp of 5700 and tint of +43. It is noticeable warm. If I adjust temp to 4300 and tint to +10, I think it is a pretty close match to the first one.

Your issue may have absolutely nothing to do with whatever color cast is being introduced by the ND filter.

When you use Auto WB you're at the mercy of the camera's programming or ACR's analytical engine. It may well be that your camera is designed to render long exposures of very dim scenes warmer than shorter exposures of brighter scenes.

Looking at the two example images¹ you linked, it appears the metallic roof on the lean-to next to the barn as well as the white building near the left edge are fully saturated in the filtered shot. The filtered shot is also much brighter overall than the unfiltered one. Any time you have a completely saturated area in the image, the way the camera or a raw conversion application does Auto WB can be thrown off. Exposing slightly dimmer to prevent full saturation anywhere in the frame can significantly shift the color temperature and WB correction the camera or raw conversion application uses to render the preview image of the raw file. So can selecting things such as "ambiance WB" or "highlight WB" in cameras or raw conversion applications that offer such settings.

The only way to check to see what is the effect of the filter is to set color temperature and white balance correction manually to the same settings for both the unfiltered and filtered photos and then compare them.

¹ Of course it is difficult to tell much from the example images when we can't even tell what image format they are in as delivered to us by google drive, much less see any EXIF info. Are these JPEGs you exported before uploading? PNGs? TIFFs? Or did you upload actual ARW files and google is converting them with whatever unknown default settings it uses to interpret what we are seeing?