In the TOS timeline Kirk was a lieutenant and student instructor while still at the Academy...sometime around 2253 or 2254, just before graduation. That means he was probably already a lieutenant like Saavik when he first boarded the Farragut on his first deep space assignment.
It's a little confused.
Dialogue from "Court Martial" specifically establishes that Kirk's service (at the rank of Ensign) on the
Republic would have to have preceded his tenure as instructor at the Academy -- active starship duty (though perhaps not classified as "deep space"), then returned to take the instructor's post.
Dialogue
also establishes ("Obsession") that the
Farragut was Lieutenant Kirk's first deep-space assignment and his first after graduating from the Academy. (Using the U.S. Naval Academy as a model, a graduating Cadet would receive an Ensign's commission.) There's already conflicting information long before J.J. & Co. enter the picture, even if Garrovick had also been Kirk's commanding officer on the Republic, a detail never established anywhere.
So is Spock an upperclassman/instructor or a commissioned officer returned to take an instructor's post? Beats the shit outta me. I'll have to wait and see whether it's explained.