My guess is that Zodiark wasn't trying to. From Altima's crystal line in Etched in the Stars, the tempering started pretty much instantly on summoning. Remember that the only primal we've had a proper, full conversation with, Ramuh, was tempering the sylphs explicitly against his own will. It seems like tempering is just a natural effect of a primal's summoning and existence, regardless of intent.
Uhm... no, actually. I think you're thinking of a different cutscene. I'm thinking of the Echo flashback of Elidibus in Anamnesis, before the Dream Amaurot bit. Transcribing the segment in question...
That Echo flashback is hard to completely dissect for truth, because it's clear both that A: it is depicting at least two factual events, some significant time apart, and B: it is being SUPER non-literal, what with the lack of cuts and black background. But what is clear is that Elidibus definitely did possess an archetypal hero of the Sundered (post-Sundering, of course), specifically to rejuvenate himself. The mystery is when and where exactly this happened, and what may have happened beforehand in that world, but neither of those are tremendously important to figuring out the chronology of Elidibus' life. The only evidence we have suggesting anything on that is that a figure that looks like the FFI WoL appeared in the First's history, but given the same armor exists in the Crystal Tower somehow, it's hard to say that's a definite A-to-B line to draw.Ancient Elidibus looks at his own hands as they fade.
"It fades. Fades away into oblivion. Does the world no longer have need of me?"
"No. I am Elidibus. And I must--I will fulfill my duty."
Camera pans to FFI WoL-looking guy, facing away from camera.
"Sundered though you may be, you fought for the world's salvation. For hope. Hope..."
Elidibus reaches out the FFI WoL-guy, cuts to black.
"Ahh, it swells within me. Empowers me. Now--now I may carry out my mission."
"Why do I yearn for this? Why must I struggle so?"
Saying Azem is somehow involved actually has far less grounding.