I think ZXC didn't want ZYL in the position, but once ZYL applied he couldn't block him without looking bad to outsiders/making the tensions between them obvious. And not even Minister Gao, who's known ZXC for a long time, has any clue about it; ZXC maintains the image of normal family relations. So he supported his application, and to everyone else it probably looked as if they'd been acting in concert ...