I'm not an umpire, but hopefully I can answer this.
NO, it is NOT correct. Under all rule codes that I am aware of. Oddly enough, this is the third time that I have seen or heard of an umpire doing this.
This appears to stem from misapplication of the rule about "unannounced substitutions" (OBR) or "unreported substitutions" (FED).
First, the rule is written slightly differently in high school (FED) and pro (OBR).
In OBR, Rule 3.08(a) states that: If no announcement of a substitution is made, the substitute shall be considered as having entered the game when—(1) If a pitcher, he takes his place on the pitcher’s plate; (2) If a batter, he takes his place in the batter’s box; (3) If a fielder, he reaches the position usually occupied by the fielder he has replaced, and play commences; (4) If a runner, he takes the place of the runner he has replaced.
So if your game is being played under OBR, then a player would actually have to get on the pitcher's plate (rubber) in order for a pitching change to happen. HOWEVER, as I point out in the next reply, the rule is not even applied completely verbatim in MLB.
FED is similar, but adds one very important qualifier. Rule 3-1-1 states: Should there be no announcement of substitutions, a substitute has entered the game when the ball is live and:
a. a runner takes the place of a runner he has replaced,
b. a pitcher takes his place on the pitcher's plate,
c. a fielder reaches the position usually occupied by the fielder he has replaced, or
d. a batter takes his place in the batter's box.
Again, a new pitcher would have to actually get on the rubber, AND the ball would have to be live under High School rules.
I really haven't looked up NCAA rules, but I doubt that they are very different.