I think I see the issue. We are using different timeline dates. Chabad dates the destruction of the First Temple to 423 BCE, with construction of the Second Temple commencing in 353 BCE and finishing in 349 BCE. Other sources put the dates at 586/7, 538/9, and 516 BCE respectively. Therefor the date in the Chabad link is correct for the timeline they use.
I thought that might be the case, but wasn’t sure. The ‘missing years’ is quite a subject on its own.