

The reason you see tones move toward the shadows is probably a consequence of trying to reverse the effects of haze. Compare that to Contrast or Tone Curve where the type of image doesn't matter the same curve will always affect the image numbers and histogram in the same way. So different image content creates different results, like the other three corrections I grouped it with. But Dehaze goes beyond that in using its physical model of haze to try and recognize 3D distances in the image and making larger corrections to what it thinks is more distant haze.

Dehaze is more like Shadows, Highlights, and Clarity in that the changes it makes depend on what tones are near other tones in an image (it is somewhat content-aware). Looking at the histogram alone won't tell you how Dehaze works, because it isn't simply redistributing the histogram like a Contrast or Tone Curve adjustment does.
