The Cradle was a losttech supersoldier factory in the Olivie's era, as it takes in babies and implants some kind of core into them(hence the name, it's literally a baby upgrade machine), which also makes them qualified as administrators/pilot/power source for the giant battleship. Olivie however, was born inheriting the core from her mother, something which doesn't normally happen, and gave her a very very high affinity for administrating the Cradle.
The key element then is that Olivie had a heritable access to the Cradle, while all other core bearers died out in the meantime. Thus for Jail's purposes, Vivio only needed to be similar enough to Olivie to inherit the control core from the relic. In fact, some changes are preferred, since Olivie's lack of arms pointed to some incompatibilities, and tweaking for full compatibility would be better.
TLDR: The Cradle is a magitech Space Marine factory with the controls locked to some specific Space Marine. It's waiting for someone to match the Original so they can unlock the Exterminatus mode.
