What links tertrachs, denarii and Caesar specifically to the Rome of the Bible?

(and not the Rome we were given in history)

I don't see that link.

Where does it say that Herod is a Roman? Or Pilate? Or Augustus?

If I don't step out of the Bible and try to figure out what reign people are under at the start of the New testament, I don't come to the conclusion that Rome (a location that is mentioned a handful of times) is a huge empire under which rule everyone is living.