"The Diaspora" isn't a time period.
The Diaspora is a place; specifically, anywhere in the world that isn't Israel. Numerous powers in the Diaspora have dominated Jews; one might even go so far as to say almost all of the Western ones.
However, none of them were 'foreign', as the countries were discriminating against their own citizens.
Virtually all of them. A survey late in the 20th Century counted self-identified adherents of Judaism in almost 140 countries in addition to Israel. None of those countries is 'dominated' by Jews, and there is a strong tradition in the Judaism of the Diaspora to the effect that "The law of the land is your law." One of my Polish Jewish great-uncles explained the meaning of this tradition to me when I was no older than 4 or 5, as: "When in Rome, you must learn to talk in Romish." So it must be concluded that technically, the Jews dispersed from their land and living among the various nations have been dominated by well over a hundred different powers since the onset of the Exile.
There were no Foreign Powers
The implied powers of the president in foreign policy making is the draft. Abraham Lincoln implemented the draft during the civil war.
how to get powers
First the Assyrians, then the Babylonians, followed by the Persian Empire, the Greeks and finally by the Romans.
The United States Constitution divides foreign policy powers, there are six basic ways in which Congress can originate or shape foreign policy
setting foreign policy
It was the mighty Roman Empire that ruled in the end of the Oldtestament and the new testament as well.
Wealthy planters
It was the two leading European superpowers at the time...England and France.
Congress and the President share foreign affairs
The Soviet Union was ruled by the Communist and the Governmental powers of that time.