Ayanami and Yuuri's meeting
It happens during the exam battle. Ayanami comes to overlook just as Yuuri is battling with the rest of the team.
Ayanami soon notices that Yuuri's Zaiphon is... weird, for lack of better words. It glitches slightly, but when his Zaiphon does come out, it's explosive and powerful.
What Ayanami notices too is that Yuuri's attitude in battle is different than everyone else. He's not aiming to kill, or even hurt. He's mainly protecting others, and sometimes getting himself flying around because of his glitching Zaiphon.
To Ayanami, it is almost certain Yuuri is not really made to be a soldier. He asks about the boy's reasons to be here, and learns that it isn't by free choice, that the chairman is the one that made Yuuri enroll and it's always been obvious to the teachers that Yuuri is not happy to be here.
As the battles continues, Yuuri has had enough. It manifests in a wave of Zaiphon that forces everyone to the ground but Yuuri. The people outside the room (Ayanami's included) are not affected, but they do feel the shockwave (like a breeze).
Once more, it is obvious to Ayanami what Yuuri did. Unwilling to see anyone hurt, he's stopped the battle by forcing down all participants. His comrades aren't too happy, while their opponent is hesitating in attacking again.
The person overlooking the examination opens the door to tell Yuuri the examination is finished only when their opponent is killed. That doesn't go well with Yuuri, of course.
He's not in Maoh Mode (he's got enough sense not to let himself show his powers) but he angrily declares it is not needed. Ayanami senses there's something just there in Yuuri (his Maoh powers) and decides to try and trigger him.
He means to kill the opponent, but the unexpected happens. There's a time lapse between the moment Ayanami's Zaiphon wraps around the opponent's neck and when he kills him. It's short, but well-
Yuuri has fast reflex, especially when a life is in danger.
Yuuri's own Zaiphon makes a smaller circle around the opponent, and when Ayanami's Zaiphon tries to close in, it's stopped by Yuuri's. In this moment, Ayanami can feel there is something stronger within Yuuri, something that manages to make Yuuri's Zaiphon strong enough to counter Ayanami's.
Ayanami stops his Zaiphon, and while there is a spark of anger, he is more interested than anything. He understands why the chairman took Yuuri. Whatever this power is, it will be useful.
What startles Ayanami is the furious look he receives from Yuuri. Once more, Yuuri prevents himself from turning Maoh, but this time he's on the edge. While his eyes and hairs do not change, his gaze itself is different.
Yuuri actually marches to Ayanami, standing in front of him with obvious anger radiating. Ayanami makes a subtle gesture to prevent his men from interfering though, as he's curious to see what happens.
And then, Yuuri basically scolds Ayanami-who notes Yuuri's voice is slightly deeper. Ayanami's men are amused, everyone else is shocked.
Ayanami? He offers right there and then to take Yuuri as an apprentice. That, of course, makes Yuuri fall silent and looses his anger to shock. What makes Yuuri accepts is Ayanami adding in a whisper that if he wishes to escape the chairman, Ayanami is the best choice.
Somehow, Yuuri feels it's a good idea to accept, and so he does. This ends the story of how Yuuri ends up on Ayanami's ship!