The temporal order for sequential computation of posteriors is just our interpretation, it is not a part of the formalism. If we get pieces of evidence e1, e2, ..., ek in temporal order, we could do Bayesian updating in the temporal order, or the reverse of the temporal order, and the formalism still works (that is our overall posterior will be the same, because all the updates commute). And that's because Bayes theorem says nothing about time anywhere.