It seems that more often than not, when the Watch Tower Society says something about biblical chronology, they're probably wrong. This seems to be the case even for uncontroversial matters! Insight on the Scriptures volume 1, page 584 states (bold formatting added):
Nehemiah 12:22 mentions the recording of Levitical heads of paternal houses “in the days of Eliashib, Joiada and Johanan and Jaddua . . . down till the kingship of Darius the Persian.” Since Eliashib was high priest at the time of Nehemiah’s return to Jerusalem (Ne 3:1) and since by the time of Nehemiah’s second visit to that city (following the 32nd year of Artaxerxes [443 B.C.E.]) Joiada had a married son (Ne 13:28), it is likely that the “Darius” mentioned was Darius Ochus (also called Nothus), who ruled from 423 to 405 B.C.E.
No, Watch Tower Society. The conclusion that the "Darius" mentioned here is Ochus is not "likely". It's wrong.
Eliashib, Joiada, Johanan and Jaddua were priests who officiated consecutively (for 37, 23, 39 and 51 years, respectively) from 470 BCE until 321 BCE. Whilst Joiada and Johanan's periods each had some overlap with Ochus (who did indeed "rule from 423 to 405 B.C.E"), Jaddua didn't at all. The only 'Darius' contemporary with Jaddua was Darius III Artashata (336 BCE - 330 BCE, also called Codomannus).
Morons.