Possible In-universe explanation: when we see Spock serving with Pike, he is younger and more inexperienced than when we see the more reserved Spock of the Kirk era. The younger Spock was perhaps overcompanstating a bit, trying to find a way to fit in better with all the emotional humans he was stuck hanging around with. We see much the same sort of behavior with Saavik in STII later on (though by the time we see her in STIII, she's apparantly decided to exercise a lot more self-control in public).
Agreed. As can be expected of those that are mindful of improvement and developing as people and professionals, Spock had matured by the time he became 1st officer. Referencing that key mother-son moment from Journey to Babel, Amanda described how Spock, as a boy, would be out of sorts after facing the ridicule of his peers. Those peers were undoubtedly Vulcan boys, not half human/half Vulcan. With that one can see that maturity and discipline go hand in hand with Vulcan culture, and that both are attained over time.