I'd think "Coming of Age" as a genre category would only include stories that focus exclusively on growing up in high school. "Coming of Age" as a tag would include any story that dealt with younger kids growing up (though used mostly for those still in school).
I agree with what I think is your intent, that "coming of age" refers to the process of the child turning into an adult, but disagree with the phrasing. At best, using high-school as the focus limits the tag to those stories which take place around the 1950's or later.
During the war years and interregnum, coming of age stories usually had boys, 16 - 19 years of age, going to war. Prior to 1914, coming of age stories had been similar since the rise of children's literature in the mid-19th Century: adventure stories starring adolescents.
The classic example of a coming-of-age adventure novel written for children would be Treasure Island. The age of the protagonist, Jim Hawkins, is never explicitly stated, but is inferred to be 12 or 13 based on standards of the time.
Classically, much of the adventure and coming-of-age genres involve pre-adult characters being thrust into adult problems and situations. This gets complicated as the social idea of children was different to ours, and there was basically no concept of an intermediary phase such as we see teens, but the key point is that for any novel written, or taking place, prior to the early 20th century the age of adulthood would usually be 14 - 16.
Where I do think your distinction is important is with respect to Do-Over novels. While some authors do play with the concept of body shaping mind, most Do-Overs involve mature minds in teen bodies, so any personal growth they achieve should be considered a delayed acceptance of responsibility rather than a coming-of-age.