>>15210700It has absolutely NOTHING to do with real-world time, and everything to do with your Rank and what Writs you have active.
Writs of Challenge raise the levels of all trainers in the Chateau by 5-20 depending on color. (Base, Red, and Black).
The higher ranked the trainer, the higher the level their Pokemon (up to Marquis and Duke, which start off at 40-50 before writs).
If you ignore the Battle Chateau and never rank up, you will never see anything higher than level 20.