In order to win you need to feed the monkey until the hunger meter is completely full. Try to use as many desserts as possible at once.
When Rhee is full, she’ll start filling up the reward chest. This might take a while. The timer will show you how much time is left before you can pick up your prizes. You cannot start feeding Rhee again while she’s filling the reward chest.
If you want to claim your reward instantly, you can speed up the process by spending some crystals. When the monkey’s done, you can get your goodies from Rhee’s window.