SO I've seen tons of Backer Beta videos. Most notably the town of Dyrford is the centre of the beta, so I've seen it even more times than I could count. So what about it?
According to the wiki, Dyrford lies on the banks of Bael River.http://pillarsofeternity.gamepedia.com/Bael_River
According to the map of The Reach, Bael River has its estuary into the Bay of Crowns, which is south of the Dyrwood.http://hydra-media.cursecdn.com/pillarsofeternity.gamepedia.com/d/d8/WorldMap.jpg
So I figure that the river you see in the game, the same one that runs the mill, is in fact Bael River. Why then the current of the river is from south to north, instead of north to south? The movement of the mill is the key here.
I doubt that this particular map has cardinal directions mixed, so I call shenanigans