ATTN: Star Trek fans, I am confused!?

Yes...In fact , in the scene when Kirk meets old Spock, he asks "Where you come from did I know my father?" Spock says that he did and that his father lived to see him command a starship. Since Enterprise was his first command, it can be umed that Kirk's father lived at least to 2264 - the year Kirk supposedly took command of the Enterprise (in the original timeline).