To be fair to Cushman, this is what he writes (on p.173 of the first edition):
Day 2, Thursday. The first full day of production was also spent on the bridge, with the camera rolling between 8 a.m. and 6:50 p.m. Daniels was one-quarter day behind when he took his last shot. Two scenes had been postponed and would be filmed during production of the next episode -- "The Naked Time." One was the brief shot in the teaser, of Spock in the command chair and the unusual placement of Lt. Uhura and Lt. Leslie at the helm -- the plot for "The Naked Time" explaining why. With the addition of the Captain's log entry that opens the episode -- not in the shooting script, but written and recorded later -- Roddenberry felt the audience needed to see Spock on the bridge when Kirk refers to him. He was right. The second scene -- Kirk's first visit to the bridge in this episode -- features Bruce Hyde (as Lt. Kevin Riley) at the helm, a character introduced in the next episode.
So, Cushman correctly identifies the shots with Spock, Uhura, and Leslie on the bridge that were taken during production of "The Naked Time."
Given the fact that the scene wasn't in the shooting script, I wonder if it was really "postponed?" It makes more sense to me that it was only decided to do that pick-up later (or, alternatively, those were just alternate takes from "The Naked Time" dropped into the edit of "The Man Trap" to make it work, and not episode-specific pick-ups). But, that's just speculation at this point.