That's true, but that global state of the universe can be written in terms of its reduced states on spatial subsystems. From this perspective we can talk meaningfully about propagating superpositions. For example, take a toy example in one dimension with three spatial subsystems A, B and C representing disjoint intervals arranged in order. Immediately after a splitting event the combined wavefunction over all subsytems might be:
(psi_1 + psi_2)_A x phi_b x rho_C
(ignoring normalisation for convenience) then after a certain amount of time it becomes
(psi_1 x phi_1 + psi_2 x phi_2)_AB x rho_C
and then eventually
(psi_1 x phi_1 x rho_1 + psi_2 x phi_2 x rho_2)_ABC .
Now, all of that is certainly happening within the realm of some joint superstate, but it still makes sense to talk about how fast the split propagates, surely?
(psi_1 + psi_2)_A x phi_b x rho_C
(ignoring normalisation for convenience) then after a certain amount of time it becomes
(psi_1 x phi_1 + psi_2 x phi_2)_AB x rho_C
and then eventually
(psi_1 x phi_1 x rho_1 + psi_2 x phi_2 x rho_2)_ABC .
Now, all of that is certainly happening within the realm of some joint superstate, but it still makes sense to talk about how fast the split propagates, surely?