In Nehemiah chapter 12 there is a list of the high priests that served in the second temple. The last one mentioned is Yadua in verse 11. According to wikipedia Jadua was in the times of Alexander the great and even met each other (the famous legend of Alexander seeing Shimon hatzadik in his dream according to Josephus was Yadua, and some even think that they are the same person).
Since Yadua is mentioned in the book of Nehemiah it follows that the book wasn't completed until the days of Alexander the great. So my question is, is this compatible with Jewish tradition, are there any Rabbinical sources that state that the book of Nehemiah was completed before that?