The saxophone is pretty much an “imperfect” instrument. So some notes are in tune while others are flat, and usually the highest range sound sharp.
For a tenor, take the middle-B (only left index finger pressed) as the reference note to tune to zero on your tuner (adjusting mouthpiece position as you’ve been told). For an alto, use the 2nd register F# (3 left fingers, right middle finger plus octave key) as the reference note.
Doing that, you’ll find -more or less, depending on the sax brand- the lower notes flat (except the 2 lowest B and Bb, slightly sharp) and the highest range, from high-C up all sharp.
Nota bene: Take into account that you’ll NOT see the “B” or the “F#” on the tuner display unless it has a key-transpose feature (very few have it). So, for tenor, playing the reference notes on any saxohone the tuner will display “A” (due to the different transposing patterns alto and tenor have).