The Lodge/McLeish model successfully fits the temperature and composition dependences of the segmental dynamics for both components in disordered styrene-isoprene tetrablock copolymers (SISI). The fitted parameters phi(self) are in good agreement with the values anticipated in the Lodge/McLeish model after accounting for the junction effect. A geometric mean mixing rule was used to average the segmental dynamics of the two components in order to describe tracer diffusion in the SISI matrices. This mixing rule accurately reproduces previously reported experimental results for polyisoprene, polystyrene, and styrene-isoprene diblock tracers. The unusual homogeneity of these matrices, as inferred from tracer diffusion measurements, is discussed in terms of thermodynamic barriers to diffusion.