Prepositional phrases are generally adverbial, but certainly not always. Sometimes it can be difficult to tell what they modify.
Take Acts 14:1 for example. Paul and Barnabas have just been run out of Pisidian Antioch and have entered Iconium. The NIV reads, “At Iconium Paul and Barnabas went as usual (κατὰ τὸ αὐτὸ) into the Jewish synagogue. There they spoke so effectively that a great number of Jews and Greeks believed.”
The Greek is, ἐγένετο δὲ ἐν Ἰκονίῳ κατὰ τὸ αὐτὸ εἰσελθεῖν ⸀αὐτοὺς εἰς τὴν συναγωγὴν τῶν Ἰουδαίων. So what does κατὰ τὸ αὐτὸ modify?
I thought the NIV was pretty straightforward. “According to the same” is adverbial, the point being that it was their custom to first go to the synagogue when they came to a new town.