I should clarify that the hypergraph, which is the state of the model, represents only space at a particular instance in time (in some reference frame). And rules operate only on that hypergraph.
From these rule applications, one can compute a causal graph, which represents spacetime. But rules don't operate on the causal graph directly, which is why the past is "protected".
Whether the past is "real", I think, is a philosophical question that our model does not answer, and it seems to me it fundamentally depends on what "real" means. To compute the future evolution of the hypergraph (on any of the multiway branches) past is not needed, so in that sense, it is not real. Whether the past can be reconstructed from the present would be rule-dependent. However, the causal (i.e., spacetime) graph can be computed from the evolution. So the past does exist in that sense.