Kai didn't do anything suspicious in his first week. He just observed the reactions of people; he wanted to know how they would react to this absurd situation.
'It seems they aren't totally under control. But how is the king subtly manipulating them? It may be related to this formation.'
Kai concluded after his observation. He started studying the formation after that.
He only did that during his work time; he didn't do anything in his free time. Staying near the Treasury all the time may arouse suspicion.
"Hey, how long are we going to be locked up like this?"
"The king didn't even give us any proper explanation. He just treats us without any respect."
"I am currently at a critical moment in my cultivation; I need to go to my house for a breakthrough; I can't even do it here because of the crowds and disturbance."
Like this, a lot of people complained about the situation. Nobody likes to be locked up for no reason.