If nothing else, he knew human anatomy and understood how the body worked. He knew how humans were different from Vulcans and well enough to explain it in an emergency situation if it came up to it. He was only familiar with the phrase because of the films and catalogued it for what it was in his head.
He didn't acknowledge her thank you, treating it for what it was. "It is recommended for at least a week, but until the skin is healed is best. I would advise coming back to change the bandage every two days," intoned Spock naturally, slipping into his research mode and giving her straight facts about the situation. He finished wrapping her hand after applying the cream, then glanced over at her.
"And if you are fighting among my peers, pay attention to those fighting near you," Spock added quietly, a bit of a smirk slipping in. He knew well how to fight and defend, but someone like Jim was always defying logic and taking risks. It's what made him a good leader, as Spock was slowly learning, but he wouldn't deny that it was always interesting fighting along side the other members of the Enterprise.