At this point, I speak in technicalities, many of which have no practical application
Even the curial bishops have a titular diocese, so they are “ordinaries” of dioceses that exist at least on paper. When acting in the name of Holy See, they are acting on faculties given directly from the Pope. When acting in the name of their office, they are acting on privileges/faculties granted to their titular see!
I’m not sure if auxiliary bishops are still given a separate formal titular see, or if they are directly attached to the diocese in which they serve, but they are only allowed to function within the diocese with the implicit consent of the actual ordinary of the diocese (except in the case of a co-adjudicator or others who’s faculties come from the pope).
The ordinary of a diocese, with sufficiently grave reason, suppress the faculties of another bishop, even the auxiliary, to preach, speak or publicly perform the sacraments in this diocese. This would, for instance, prevent our friend the excommunicated bishop from publicly claiming to act in the name of the Catholic Church, or otherwise protect the faithful of the diocese from errant teaching.
So to bring some relevance back to the original topic, I would image that “precedence” has to do with helping to distinguish to the public which bishops have authority over whom. Thus I believe the local ordinary should always be first, as he is generally the first and foremost Shepard of the faithful in the diocese, followed by the other ranks as discussed elsewhere in this thread.