So how much should you tighten your saxophone neck screw?
Just a few turns until you feel comfortable resistance, but not excessively tight. (If you overtighten, the receiver will distort and may not seal well … and the screw itself may break!)
The function of the neck screw is to keep the neck aligned so the octave key will work properly. There’s no need to crank it too tightly.
If the neck still moves when your neck screw is snug but not excessively tight, the tenon should be refitted by a skilled technician.