To be consistent with the Prime Directive, Spock should've been pissed (not literally) that they were helping at all. He should've insisted that the Enterprise just sit in orbit and watch the volcano go kablooey.
Well maybe he DID. We just didn't actually see that conversation take place. Maybe he did put all this forward, but his opinion was over-ruled by Kirk's decision to go down there and help people.
I mean, we know for a fact Scotty had reservations about certain aspects of the plan too (even if he might
have sided with Kirk about the actual sentiment of saving lives). But his opinion is just an opinion, he isn't the Captain. Neither is Spock.
Ultimately, the chain of command on a starship is an autocracy. It's Kirk's call what they do, no matter what Spock (or anyone else) says. If there's a post-mortem of the decision process, that's up to the brass at home, to decide whether Kirk made the right decision retrospectively, and to praise or punish him accordingly.
This is true of TOS itself as much as it is the JJ films.