I was thinking some more about this, when i was walking in the park and:
When using automatic, the newly created Face, if the adjoining Faces have different Materials, has to be either one of the Materials..when the Bevel has two Segments as Omar suggested, it is easy:

So, the question is, how does Blender decide which Face it will use the Material of?
It appears, that it looks at the Indices of the Faces and whichever Index is closer to the Index of the newly created Face, will be used. In your case:
