We are now studying the Fourth and Fifth Centuries after the life, death, and resurrection of Jesus. The capitol of the empire had indeed moved East some twenty years before Saint Ambrose was born and some forty years before the birth of Augustine. The center of the Church moved to Constantinople as well. But Rome had Her graveyards of saints. Many, as we know, were turned into churches; two examples being Old Saint Peter's Basilica and Saint Bibiana. Rome and the West were still a major focus, and it is into this setting that Ambrose and Augustine strengthened Christianity.
Here is "Veni Redemptor Gentium":