What a great first puzzle and nicely related to real life! I can solve it in at most

5 presses

Like so

Notice that the key is to get to the off position. Once in off, we know exactly what state we are in and how to reach any other state. From off the most is 3 presses to reach high. If we start in high then we just need one more press to reach off, so we need at most 4 presses to reach anywhere from high. If we start in medium then we need two presses to reach off, so we need at most 5 presses to reach anywhere from medium. Now if we start in low then we need 4 presses to reach low and 5 presses to reach medium. For reaching high (when starting in low) we can use a clever trick: if we could do 2 presses without reaching off then we must be in high. In all the cases we only need at most 5 presses or 2.5 minutes.

What a great first puzzle and nicely related to real life! I can solve it in at most

5 presses or 2.5 minutes

Like so

Notice that the key is to get to the off position. Once in off, we know exactly what state we are in and how to reach any other state. From off the most is 3 presses to reach high. If we start in high then we just need one more press to reach off, so we need at most 4 presses to reach anywhere from high. If we start in medium then we need two presses to reach off, so we need at most 5 presses to reach anywhere from medium. Now if we start in low then we need 4 presses to reach low and 5 presses to reach medium. For reaching high (when starting in low) we can use a clever trick: if we could do 2 presses without reaching off then we must be in high. In all the cases we only need at most 5 presses or 2.5 minutes.