To have multiple fills that way you need multiple paths. You may:
1) Create the basic (circular) path with no stroke and Ctrl/Cmd+C+F to make a copy in front;
2) Create the partially overlapping path with no stroke;
3) Select the copy path from 1) and the path from 2) and Pathfinder>Intersect (depending on version you may need to hold Alt/Option) to create the top path;
4) Group 1) and 3) and in the Appearance palette tick to select Group, then in the flyout tick Make New Stroke and drag it down below Contents and apply twice the Stroke Weight you want visible.
If you have corresponding multiple sets in the same Layer, you may apply the new stroke to the layer.
I would build this as a Live Paint object:
- Make a circle with the fill and stroke you desire.
- Add a stroke on top for the shadow line with no fill or stroke.
- Select both object and convert to "Live Paint" (Object>Live Paint>Make.
- Select "Live Paint Bucket" tool, choose a darker red and click in the shadow area to fill it.
Now you are free to move the shadow line anywhere in the circle and the color areas will update automatically.
Live Paint is very powerful and is too often overlooked, in my opinion.