I haven't studied the physics of the Seebeck effect at all, but my guess is that it has to do with how temperature affects how easy it is for electrons to enter the conductance band. The electrons have to jump to different energy levels as they transition between different metals, and I imagine this may be temperature dependent. If this is true, then even a coating of one atom thick should have an effect. This would also be consistent with the large effect of copper oxide.
You always need two junctions for thermocouples (which use exactly the same physics): the hot junction and the cold junction. Energy flows from the hot junction to the cold junction. The hot junction could for example be the copper-nickel junction at the positive input terminal, and the cold junction could be at the negative input terminal which is 0.5 K colder because it's directly connected to the case (random example). The current flows between the two junctions (terminals), causing an offset voltage.