They weren't Jews they were Israelites. Jews only came from the tribe of Judah, there were eleven other tribes. Paul was not a Jew, he was a Benjaminite. Caleb was an Ephraimite. Abraham wasn't a Jew, Isaac wasn't a Jew, Jacob wasn't a Jew, Moses wasn't a Jew he was a Levite That is correct, however, the people who lived in those two kingdoms encompassed the people commonly known today as the Jews (of all tribal ancestry, and none of the those living in the House of Israel became "Gentiles".
Yair Davidy, an Orthodox Jewish man living in Israel is widely known and accepted as an expert in the scattering of the House of Israel and where the tribes went. There were hundreds of thousands of Israelites carried away by the Assyrians into the empire and assimilated with the gentiles of the regions.
Yair has published many books that are excellent in scholarship. Look him up for a good read and a good education on gentile assimilation.