The podcast deals with Ezra Chapter 7: the arrival of Ezra in Jerusalem about 458 B.C.
(The previous chapter Ezra 6 presents Darius I as the king. He is the king that 'accidently' threw Daniel into the lion's den.)
Halley's Bible handbook clarifies that the King Artaxerxes in Ezra Chapter 7 is really King Artaxerxes I - a different king from the "earlier" King Artaxerxes (King Cambyses) - who stopped work on the temple during Ezra Chapter 4 - years before Ezra was born or had arrived in Jerusalem.
Apologies for any misunderstanding during the podcast reading: these historic names are a little confusing.