http://www.aish.com/jl/h/cc/48938582.html
...The rebuilding of the Temple, which had began under Cyrus when the Persians first took over the Babylonian empire, and which was then interrupted for 18 years, resumed with blessing of Darius II, the Persian king whom we believe to be the son of Esther.
The work is completed in 350 BCE and the Temple is re-dedicated...
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.
AHA! Eureka!
Awesome.
: )