Reconfigurable Intelligent Surface (RIS) assisted physical layer key generation has shown great potential to secure wireless communications by smartly controlling signals such as phase and amplitude. However, previous studies mainly focus on RIS adjustment under ideal conditions, while the correlation between the eavesdropping channel and the legitimate channel, a more practical setting in the real world, is still largely under-explored for the key generation. To fill this gap, this paper aims to maximize the RIS-assisted physical-layer secret key generation by optimizing the RIS units switching under the eavesdropping channel. Firstly, we theoretically show that passive eavesdropping significantly reduces RIS-assisted secret key generation. Keeping this in mind, we then introduce a mathematical formulation to maximize the key generation rate and provide a step-by-step analysis. Extensive experiments show the effectiveness of our method in benefiting the secret key capacity under the eavesdropping channel. We also observe that the key randomness, and unmatched key rate, two metrics that measure the secret key quality, are also significantly improved, potentially paving the way to RIS-assisted key generation in real-world scenarios.