Obito placed his chakra rods in all of the jinchuuriki he used. Seeing how they were already dead, just like nagato's paths of pain. The chakra rods transmit the will of their user since the dead have no will of their own, the chakra rods allow you to control them completely. The reason that both Obito and Nagato's paths share their eyes is because when you put chakra rods into the corpses they become an extension of you (paths). So when Obito had the Gedou mazo absorb his paths, the Juubi also became an extension of himself.
Well, that's all let me know what you think of this explanation or whether you have another theory down below