Spock was absolutely radiating jealousy from every word, look and bit of body language
http://www.youtube.com/watch?v=BWg1BTCnAA4
Ok, yeah, looks like it, but that is not what's going on. (note... I can't believe I'm having a K/S debate... for the record, I don't even get on board with (aka 'ship) that, but carryin' on...)
At first, sure, but it's Spock being *suspicious* first and foremost as to why Carol is even being allowed to come on board. He is, as we all know, a hella smart person. And also not nearly as controlled in his emotional department, as his carryin' on with Uhura shows, so there might be a hint of uncomfortable due to the recent crap and perhaps a little unsure about his position as well... but that was not anywhere near jealousy. She is *superfluous*, and that makes him suspect her even being there in the first place.
But Kirk's the Captain, and he's the First Officer/Science Officer, so he can't really tell him no on this one. She comes along. And he discovers and uncovers her ruse due to his suspicion.
/But on top of that, he's got Uhura. Like she's gonna let Kirk horn in on her man. As if.
//Or hell, maybe you're right, he's hella jealous and uncovers Carol's real nature in the hopes Kirk will rush into his arms and slip him the tongue like Spock is some sorta Big Damn Hero. What do I know.
///Now, being as Zachary Quinto has come out as a gay man, perhaps in real life he couldn't help himself but be jealous of Alice Eve vis a vis Chris Pine...