The moment that Nebuchadnezzar appears is the moment that Jehoiachin surrenders, along with his mother (see 2 Kings 24:12) and his household. The dating is from Babylonian historiography: Jehoiachin was captured in the eighth year of Nebuchadnezzar’s reign. The author of Kings clearly knows the Babylonian historiography.
12 and Jehoiachin the king of Judah gave himself up to the king of Babylon, himself and his mother and his servants and his officials and his palace officials. The king of Babylon took him prisoner in the eighth year of his reign