It is clear that there is a conflict with this reference by Josephus. Some accept the 13 years as credible but dismiss the dating to year 7 of Nebuchadnezzar, and with reasonable basis. But there are other references to consider including Isaiah 23:15 which says,
"And it must occur in that day that Tyre will be forgotten 70 years."
This, of course, links the desolation of Tyre with the other nations that were to be desolated and serve for 70 years. Thus this reference would end the siege of Tyre in year 23, the final campaign year of Nebuchadnezzar when he also deported the Jews off their land, the last deportees also being stated to serve Babylon 70 years while the land was desolated.
Another factor consistent with the siege occurring after Jersualem was destroyed is Jeremiah 25:29 where is says after mentioning Tyre among other nations to drink the bitter cup of Nebuchadnezzar,
"For, look! It is upon the city upon which my name is called that I am starting off in bringing calamity..."
So the Bible would again confirm that Tyre's siege did not likely begin in year 7 of Nebuchadnezzar but after the fall of Jerusalem in year 19 of Nebuchadnezzar. The specific edit in the 11th year of the exile of Jehoiachin was not year 17 of Nebuchadnezzar but year 19, the year Jerusalem fell. We must keep in mind that Jehoiachin was exiled on the very last day of the 8th year of Nebuchadnezzar. So essentially his years of exile match the years of Zedekiah which is an 8-year difference in comparison to the rule of Nebuchadnezzar. That is, quite simply, year 11 of Zedekiah is equivalent to year 19 of Nebuchadnezzar, not year 17.
With that in mind, and with the desolation and deportation at the same time many other nations to serve 70 years taking place in year 23, the siege of Tyre would not have been more than 3-4 years, as difficult as it was. After Nebuchadnezzar that completely emptied the land, including destroying Troy, he felt great and bragged about having conquered everything and so the next year God smote him with 7 years of madness, though his kingship was preserved for him. At the very earliest if this began in year 24 he could have been active on the throne again by year 31 BCE.
Egypt was not to be punished for 70 years but only 40, so when that time came up, we find Nebuchadnezzar going on another campaign in his year 37 down to Egypt. Those in exile from Tyre would not be released to return and rebuild until the 70 years of exile were over in the 1st of Cyrus. I know there are other theories about this, but other than this would contradict Scripture.
See part 2, cryptic reference to Babylon