No sax plays in tune top to bottom. Find a good note on the saxophone that feels centered (g, a or b might work well) and then get the reference note on the piano/keyboard etc and adjust the mouthpiece so that you can play the note without lipping up or down too much. The tuning will change as the instrument warms up so you might have to retune. Room temperature will also affect the pitch.
Playing in tune from top to bottom requires lots of adjusting, that's the tricky thing with saxes. Many people tighten their embochure when they play up the octave and end up playing way sharp up there. If you are uncertain about the tuning, playing with a reference track can be helpful. You could create a keyboard guide track of a tune you want to learn. Or, if you get the chance, play in unison with someone who plays very well in tune. A good intonation exercise would be to play octaves up and down chromatically or do octaves with scales that you are practising. If you are not sure whether you are in tune doing these exercises, initially use a tuner. But eventually you want to trust your ears. However, occasional sessions with a tuner can be revealing, they are also helpful when you check out a new instrument. I sometimes use a tuner when I feel something is not quite right, but it can get frustrating. Don't start looking at your tuner whilst playing a tune - it will be terribly intimidating! Unless you want to play classical music tuning is relative. I absolutely agree with what Pete said.
A good degree of control is necessary, but if it was 100% in tune top to bottom it would sound weird. Once we autotuned one of my husband's recordings for fun, and the result was shocking: The saxophone sounded like a synthesiser, entirely dehumanised!