“How did the secular historians make a 165 year error in dating the destruction of the First Beis Hamikdash?”
The “secular historians” didn’t make a mistake. The Seder Olam Rabbah allocated too few years to the period of Persian rule. The “secular histories” all match up with contemporary accounts from Assyrian, Babylonian, Persian, Greek, and Roman sources, while the Seder Olam Rabbah was written many hundreds of years later.
This presents no halachic or haskafic problem because there is no chiyuv to accept any particular midrashic work as literally true. R’Yose wasn’t writing a history, he was writing a midrash. Josephus was the Jew who wrote histories!