I think the standard thing about saxophone vibrato you read from tutorials all over is moving the jaw up and down in a vertical motion. At today's pratice session, I realized that the way to generate vibrato is actually quite different across the registers - the low notes seems to do better with vertical motion of the jaw, but at the higher notes, doing that is very tiring - for me - and I actually found that rolling the lips forwards and backwards seems to be much easier, smoother and less wearing.
That said, I still have not yet reached the stage where I can actually do vibrato properly, only got taught the week before xmas. I'm still doing the vibrato practice routines against a metronome. Need to talk to my teacher about this.