No, it is as I wrote. Now in Shushan the palace there was a certain Jew, whose name was Mordecai, the son of Jair, the son of Shimei, the son of Kish, a Benjamite;
Esther, Catholic chapter two, Protestant verse five,
as authorized, but not authored, by King James
boldness mine
After the kingdom of Israel was taken into captivity by the Assyrians what was left of Benjamin and the Levite priests who escaped Israel and fled to Judah became Jews. The northern 10 tribes (9 but Joseph counts as 2) known as The Kingdom of Israel were never Jews.
The lost ten tribes were not taken over by the Medo-Persian Empire. These were originally from the southern kingdom of Judah, aka Judaea.
Mordecai was considered a Jew, because he was from Judah. He was one of the captives taken when Judah fell to the Babylonians.
The kingdom of Judah consisted of the two southern tribes, Judah and Benjamin, either of which would have been called Jews because of their nationality.