It is up to you whether you use a subordinate clause or a participle construction in Latin. Both is possible!
How you use the participle depends a bit on how you word the Latin sentence. I would translate “stepping aside” as alicui decedere, “to give way to someone.” If we do that, it means the subject of the subordinate clause (X came) occurs also in the main clause (gave way to X), and so an ablativus absolutus is uncalled for. The construction becomes very simple:
Venienti Iulius decessit.
As he came, Julius gave way to him.
But if you prefer, you can construct the predicate of the main clause without referring to X again, as in English. In that case the subject of the subordinate clause does not occur in the main clause and you need an ablativus absolutus:
Eo veniente Iulius via decessit.
As he came, Julius gave way.
As for which conjunction to use, cum seems the best fit. The English “as” in this case means exact simultaneity. Julius stepped aside exactly when the other person came, perhaps even slightly before, but definitely not a second later. Therefore postquam seems inappropriate. Dum simply does not apply, as far as I can see.
If it were a coincidence that X just happened to be coming along as Y was engaged in some asidestepping business of his own, then this would be a case for the cum temporale (subordinate clause in the indicative). But it stands to reason that X's arrival was in fact what prompted the stepping aside—that is, the two actions are almost (if not in fact) causally linked. Therefore the situation calls for a cum narrativum (vel historicum). In practice this means that the subordinate clause is in the subjunctive:
Cum veniret, Iulius ei decessit.