But psychological effects have a physical manifestation.
As for the temporal separation, that would probably be a more philosophical discussion on the nature of "cause" and "effect".
I think it is worth making the distinction, because, as mentioned above, an invariant measurement of c does not imply RoS; it is an invariant measurement of c plus RoS which results in RoS; with the latter being circular in nature.
I should, more precisely, have said, I don't see the relevance of using a transformation that is not the Lorentz transformation. As there are two interpretations of the Lorentz transformation, one which incorporates RoS and one which doesn't; with one of those being, arguably, circular in nature.