It rather depended on the empire and what their philosophy of imperial rule was.

For example, according to Marco Liverani (1979 "The Ideology of the Assyrian Empire" in Power and Propaganda: a Symposium on Ancient Empires, ed. M.T. Larsen, Mesopotamia 7. Copenhagen), the ancient Neo-Assyrian empire (911-609 BC) was founded on an ideology of "unbalance and exploitation", a way to exert control over other people groups. The ancient Assyrians would conquer a people group, and move the majority of the inhabitants to other parts of the empire, and then move other people into the areas they just vacated, thus keeping the massive populations of conquered peoples unbalanced so they could exploit them.

Immediately after the Neo-Assyrians, the Babylonian Empire arose, with a different take on empire. While small kingdoms arose near the end of the Neo-Assyrian empire in response to Assyrian weakness out of Assyrian provincial regions, the Babylonians reconquered them and made them client states, vassals to the Babylonian Empire (Vanderhooft, "Babylonian Strategies of Imperial Control in the West" in Lipschits, O., & Blenkinsopp, J. (2003). Judah and the Judeans in the neo-Babylonian period. Winona Lake: Eisenbrauns). When this did not work out as expected, and places revolted, rather than deporting everyone to somewhere else, the inhabitants of rebellious cities were basically enslaved and brought to Babylon, where they appear to have resided in ethnic enclaves with names based on their ethnicity. Babylonian texts record Hebrew names of people and state that they live in a region or city in Babylon called al-Yahudu, the basic translation of which would be "New Judahtown" (see K. Abraham (2010) "The Reconstruction of Jewish Communities in the Persian Empire: The Āl-Yahūdu Clay Tablets" in agai Segev and Asaf Schor (eds.), Light and Shadows - The Catalog -The Story of Iran and the Jews (Beit Hatfutsot), Tel Aviv 2011).

In contrast to this practice of conquering and deporting, King Cyrus the Great of the next empire (the Persian Empire) allowed people to return to their homelands (including the ancient Jews), and we have a record of his performing such an act in the Cyrus Cylinder, which you can read a translation of here (see lines 31-34 especially). So his particular policy was much more laissez-faire.

In conclusion, it varied based on the imperial ideology of the empire doing the conquering. Some empires displaced entire nations, others let them be as long as they obeyed and sent tribute, and others were more hands-off, but still in charge and controlling the area through provincial systems.