Sybok is full of emotion. He is Vulcan. So emotions are in there, and can even be used in a controlled way (it's not like Sybok was a raving looney of emotions, he just had a weird calling).
The character of Spock was made half human so the emotions could play into the character. It's not about concrete examples in TOS from "ticks" to shouting ("The women!"). There was a human side there waiting to go off. Instead, Spock tried to deny it or internalize it. Part of the tension in TOS (seeing episodes for the first time) was whether or not Spock would ever go off on an emotional rant. The fact that he could become more comfortable with emotions and displays of them (friendship, sentimentality) as he aged also shows he had them. TOS Spock would be too uptight and in control to "tell them to go to hell," even if that's how he really felt. In TUC, he had no problem stating those sentiments.
That the personality of TOS Spock evolved over time is alone proof that he felt, whether he showed it as often and openly as Spock in ST09 or STID does or not. Spock Prime even admits to Kirk that he's "emotionally compromised" by the loss of his mother and Vulcan. I'm sure he had his own outburst privately when he had the chance, and it didn't have to be provoked.