I'm going to posture that the Rising poem implies that Azem was struck by The Sound.

This quote here: "God-slayer struck by an echoing roar,"

So my guess is Azem left the council, was trying to fix the problem out in the world, was hit by The Sound, Azem's echo was ripped away, Zodiark and then Hydaelyn are summoned, Hydaelyn (or maybe Zodiark) repair Azem's connection to the echo, then Azem chooses to join team Hydaelyn, the events of which lead to Zodiark and Hydaelyn fighting.

I'm going to go one step further and say the Ancient connection we should be looking for is Ancient Zenos and Azem. I bet they were friends who became rivals for the seat of Azem and Zenos most likely betrayed Azem causing The Sound to wound them so Zenos could hold the seat.