Good question, Joel was never in the position of power that would allow him to put Kinga in a position of power. Best in universe guess would be that Pearl somehow arranged for Kinga to take control of Gizmonic Institute, and Synthia is likely involved.
Of course, the completely made up history of the Gizmoplex holds some tantalizing clues, but is mysteriously incomplete, ending in 1989. It is as if someone doesn’t want us to know how Kinga gained control of the Gizmoplex.
Putting all of the clues together, I would surmise that Charles Nelson Forrester is still pulling the strings behind the scenes.