Rei (and all of her "sisters") raised by the MAGI during the routine "downloads"... in true
Skynet fashion.
After all, with Akagi's brains (plural) behind the operation of the MAGI, knowing what Seele and Gendo are up to, why wouldn't the trio see themselves as threatened? While mankind turns into goo, what could possibly happen during the aftermath of the Earth in Third Impact, besides potential destruction of all hardware related to supporting the MAGI?
You could even have Kaji's chip be the root cause of the "processing error" Ritsuko or Maya notices slowly crop up. Also recall that the trio in Tokyo-3 are only one set of several MAGI systems throughout the world.
Because, after all... everyone knows what fanboys really want:
Rei-based infiltration units trying to blend in with society at several strategic locations supporting Seele, torturing Gendo for information, and eliminating obstacles which interfere with the MAGI's plans.
That, and...
Kensuke stared at the class representative, sweat streaking down his face, and fear in his eyes as Suzahara restrained his former friend. "You don't understand! They'll find us! That's what they do! That's ALL THEY DO!"
Hikari looked over to Shinji, and sadly shook her head.
"-they don't feel pity, or remorse, or fear!"
"Kensuke," Shinji sighed.
"-and they ABSOLUTELY WILL NOT STOP! EVER! Until you are DEAD!"