Right. The upside down thing needn't be too problematic. In a blog post I wrote in July I compared the pine cones to some images including this one from the Liber Floridus:
As you see, the orientation of the "stack" of scallops doesn't really matter. The same is true on some other maps, where objects are turned as required (that's where you sometimes get a "flat city" look). I added this example from the "Book of Curiosities", but as you likely know, there are many more like this.
Additionally, it just makes sense that mountainous areas are a source of water flows, that's generally how it happens.
Now I have no idea what the umbrellas are. If we go with the "mountains and rivers" approach, then I see two main options:
1) They are symbolic. They tell us something about the "pine cone" but aren't really present in reality.
2) They represent actual features.
The second point seems impossible since we're basically looking at upside down mountains with an umbrella on top. But that may just be because we picture that the object is drawn in side view. But what if it's drawn from an imagined aerial view, as if you're looking at a top-down map? In that case, the "scallops" represents a mountainous area, with each scallop being one mountain or hill... or something like that. The water flows down towards where our nymphs are, clearly the area of focus for the viewer. In that case, the "umbrellas" would be what lies beyond the mountains, from our point of view. Maybe some imagined place. This was not unheard of in authors like Ptolemy.
Or it could be as simple as this: the "umbrella" represents a high mountain, while the scallops are foothills, from where the water appears to come. This would explain the blue paint in these scallops, since certain areas would accumulate water, especially when rainy seasons are involved.