More specifically, when the Jester goes down to correct floor and brings back whatever the princess asks, she gives N amount of coins, and then there's this "random-looking" spinner of possible rewards (coins, glu gold, special items for collections). If you click on the screen, the spinner stops and some reward is given to you. If you don't click on the screen, the spinner eventually stops on its own and a reward is given.
Does the reward depends on your clicking (and timing of that click) or is it pre-computed?
The pre-computed option seems to be supported by the fact that, if the jester is too slow and thus doesn't get the bonus, the Princess screen explicitly says WHICH bonus wasn't given.