Absolutely, you need to tune your alto saxophone. Of course, there will be changes in your tuning as your embouchure gets ready and as the horn gets ready. The first step you have to take is to set the calibration of your tuner to 440HZ. Then, play an F# with the Octave key. When playing the F#, your tuner should show A on its screen. If it shows another note that is different from this, then the mouthpiece hasn’t reached its proper position. In such cases, the mouthpiece should be moved in either direction until the tuner displays the right note.  If you have a flat note, drive the mouthpiece so that the pitch would go up, but if you have a sharp note, pull out the mouthpiece so that the pitch would go down.