The fact is, they hadn't finalised much at the time of The Cage, a lot of things could change, and it's pretty much the norm in TV shows. For example in the NCIS opening episode, Gibbs meets Fornell for the first time, yet later it's been established that not only did Fornell marry one of Gibbs's ex-wives, but that Gibbs had also warned him off! And that's a show not in the fast-and-loose '60's when continuity wasn't a big issue.
However, both Pike and Number One were both very logical and business-like characters, so having Spock be the same would have actually alienated viewers as they'd be unable to relate to any of the big-three characters.
In story though, we could always just put it down to Spock's "teenage" rebellious years, which he'd worked mostly out of his system by the time Kirk took command.