In first picture, you can see an image of a lake(Bellandur lake, bengaluru, india). In second picture, you can see the flow accumulation data for the same area I made(after "fill"ing the sinks). As you can see, the water accumulates rightward of the lake where there are houses and city.
Why is this happening?
Instead of flowing rightward, shouldn't the water flow inward the lake?
To understand why, have a look at your flow direction raster. In a flat filled area such as this, the flow direction is limited to the flat filled surface regardless of whatever topography may have been present there before filling. There are alternatives to this that either apply a downstream trend to the filled surface (helps a bit) or better yet, you could decrement (breach) the DEM instead of filling to preserve the inherent topography of the area.
As to why is this happening, look at the actual values of the DEM in the area it is filling up. As the previous answer stated, if the land there is fairly flat and not far above the surface of the lake, it will flood. If it doesn't meet those two points, then there is probably an error in the way you worked it.
