^Number of fights does matter to the definition of secondary or tertiary, but ultimately it is not the quantity of appearances, but rather the emotional range as well as character development (the "quality") that represents the gap between secondary and tertiary. To briefly look at the world of
The Simpsons, characters such as Chief & Ralph Wiggum, Cletus the Slack-Jawed Yokel, Sideshow Bob, Smithers, Jeff Albertson, Troy McClure, etc, all make multiple appearances (and even have an episode or episodes dedicated solely to themselves and their "character development"), but all are labeled as tertiary. (I could go through other popular stories, etc, but suffice to say, many tertiary characters are still present during large sections of the story, they are just ultimately unimportant to the story or they lack any real character definition...that is why they are tertiary).
While I may agree that Iruka could probably be classified as a secondary character, the others (Shino, Chouji, etc) are clearly tertiary characters since they have very little importance to anyone or anything (they can be readily replaced by almost anyone since their fights, if they do fight, have little actual character development (this is definitely true of Shino and Kankuro, but Chouji's one fight did matter, but sadly he lived)).
Main characters have "full" definition (they are "round" with well defined emotional qualities, actions and responses), secondary characters have slightly less definition, and tertiary characters have little to no real definition beyond their introduction (flat and predictable). (That is not to say that main characters without sufficient definition automatically become tertiary, that simply means that the main character is boring, and the author/creator is bad
.)