When is a sub the pitcher?

[john5396]

Last night, High School Varsity, NFHS rules

At beginning of the new inning, home team takes the field. F2 was on base, so slow in coming onto the field. Substitute S1 comes to the pitchers mound and stands behind the rubber waiting for F2. S1 has not been reported to PU as a substitute yet. After about 30 seconds home coach comes to the PU and asks if S1 is in the game? Does he have to face a batter? Coach has changed his mind or maybe S1 thought coach was putting him in and he came out without instructions...

Partner and I discussed, decided since 1) he did not toe the rubber or throw warm-up pitches, and 2) he was not reported as a sub. We ruled he was not in the game and did not have to face a batter. The coach then put the F1 continuing from the previous inning on the mound.

When does S1 become the new F1? When does he become the new pitcher and is required to face a batter?