Spock follows them away from the door. Standing around it will only lead to more suspicion and Finn seems to have an idea of where the current holder of the key is.

He doesn't say anything, but he does find it heartening that so many people here are willing to work together. Of course it's something Starfleet has instilled in the officers, but he cannot expect the same from others without first observing them and though he says nothing, as they are waiting for Finn's return, Spock catches Jim's eye and gives him a gently amused look. Jim may truly have a skill for finding the people more likely to understand the logic of working together. Or perhaps the people who simply like to. Either way, he suspects this will not be the only time he works alongside Finn.