Like stated before it seems that both games' scroll the opposite way we would normally see in parallax. Very unnerving, and so far not yet explained.
It's because the mixed character/tile scrolling with normal scrolling. That doesn't work, for obvious reasons you see visually. Ys III scrolling is not like NG scrolling, save for the town area (from what I remember). NG style is supposed to have dynamic tiles for that method. And the large open areas, could have just been done with sprites. You can mix and match for whatever the level design needs. The first level of NG should have been dynamic tiles for the far BG layer. For the first out door level, the foreground should have been sprites - since the far BG is a very big/large repeating area. Not saying it's not doable, just saying it's unrealistic for a developer to go that far out of there way to do such a large dynamic tile pattern (and waste all that space in rom).
Did it actually scroll backwards?
No, it just 'repop's back into place every so many pixels of scrolling. That's what makes it look so wrong.