ok now that I see your video I see what you are encountering.
first option is to combine the two parts and then create the fillet. Then you can split them again using the flat face of the larger part so it still shows them as separate components.
another approach would be to use a sweep command. Project the edges you want filleted into a sketch. Then create a plane that intersects that path. Finally intersect the path and create the fillet you want, finally sweep the path and use the cut option.
When you click on the fillet a dialog box will come up. In that box you will see a button for tangent chains or something to that effect. If you unselect this then the fillet will only be applied to the edges you Select. So the. Select the two Edges you want the fillet to extend over and they will be formed as you expect.