I don't know if they can be considered canon, but the official star trek app has the bios of all the characters and you can read what kind of studies they did and the skills they have
uhura bios
1 2 | spock bios
1 2
(I can find back the ones for the others too if someone is interested. They were posted over tumblr by the same user)
interesting that if we go by what the app is saying here, Spock indeed graduated in a little time compared to the other cadets so when he was Uhura's instructor he had recently graduated himself (that seemed to be implied during Kirk's disciplinary hearing in the movie when the guy introduces Spock as one of their best students, meaning maybe his role as instructor was fairly recent and something he has earned thank to his accomplishments as a cadet).
If both of them got in starfleet in 2255, it's
even possible she met him when he was still a cadet.
^ That was me.
Original Spock was a very alienated person; too Vulcan to be accepted by humans and too human to be accepted by Vulcans. His father turned his back on him for not following in his footsteps and his mother, bless her heart, struggled to understand the duality of his personality.
Spock turned to logic as devoutly as he did only because it offered him the only refuge from the strain of his situation. The loneliness and the isolation from his peers would have crushed him otherwise. In the end, he also found comfort in his friendships with Kirk and McCoy and the crew of the Enterprise, the very few people in the universe who truly knew him and truly accepted him for who and what he was. And those were friendships borne in hardship and struggle and not all of them had a particularly pleasant start.
it's interesting to think that perhaps one of the reasons why he chose starfleet might be that he maybe felt more vulcan among humans.. or at least he would look more vulcan compared to his human crew mates

and I get what you mean when you say that logic sort of is his comfort zone.
What I appreciate in the new movies is that reboot Spock seems to have a more realistic idea of his dual heritage and he's a tad less on denial about it.
Even in the scene between him as a kid and Sarek, you get the idea that the little guy is not so oblivious of the fact that his own father, who is a vulcan, is damn contradictory about the whole 'no feelings just logic' thing. He pretty much calls him a hypocrite too

So there is still struggle between his sides, but his Spock is put into circumstances that perhaps open for him the possibility to find a balance that it took Spock prime too many years to find..
Then of course there is Sarek admitting that he loved Amanda: that was the icy on the cake that completed his arc in the movie.
SpockPrime is very right when he tells his younger self that his friendship with Kirk will come to shape him as a person, hence his advice to remain in Starfleet. But his relationship with Uhura will be an even greater influence overall: a chance for intimacy and shared struggle that TOS Spock would never experience in during his 150 years.
it's a circumstance we never saw Spock into and that's why it's so interesting to me.
It also is a 'what if' scenario at play in the sense that perhaps this version of these people have some sort of a second chance when it comes to some things.
Some things are worse (e.g., spock losing his mother sooner and also the destruction of vulcan) but others are better.
In that sense, Spock is the only person on the ship who is even in the same LEAGUE with her intellectually. Consider, then, that Spock has everything Uhura needs in a relationship: he has an encyclopedic memory to keep her intellectually stimulated, and a very... er... logical approach to keep her other parts stimulated. Conversely for Spock: Uhura is smart enough to hold a conversation with him, AND she looks like Zoe Saldana. He'd be crazy to pass that up.
she's an emotional caring human who loves logic and can still keep her cool as a human. Not so hard to see what he saw in her because both his sides would be attracted to her essentially.
In a sense, she's a nerd like him but not the stereotype of one. She complements him as he's his opposite when it comes to being social because we see in the movie when her character is introduced to the audience that she gets in a bar as if she owned that place and other cadets greet her with smiles and she gracefully moves through the tables to say hello to her friends. She orders a hella lot of drinks too (I dunno if they were all for her, or she was ordering them for her friends too).
Then the scene with Gaila tells us that she's someone so focused on her work/studies who would spend her nights in the long range sensors labs (like I joked before, she probably is the type who would have no problem telling her boyfriend that she has work to do in the lab and they can't go on a date. And Spock being Spock would be fine about it and not take offense, he'd like her even more

)