I'm a bit confused by your question. It is called a subtone when one plays notes in the low register with a looser embouchure and the jaw pulled back to make the notes soft and "breathy" sounding.DeUtCheaxelplaya said:
It is called an overtone or harmonic when one fingers a low note on the saxophone and by altering the shape of the throat and the speed and direction of the airstream forces the note to sound an octave higher, an octave and a fifth, two octaves, and octave and a tenth etc., etc. with the same fingering.
When one plays these overtones or harmonics on notes above high F (3rd leger line above the staff) using special altered fingerings, they are called altissimo notes.
You said "when you match your normal tone to the overtone---does it matter when the intonation is off". By this I take it that you mean like when you finger low B natural and make it sound its first overtone 3rd line B using the same fingering that it has the same pitch as B natural fingered with the first finger.
On well made saxophones with the correct mouthpiece placement and the proper input pitch of the mouthpiece the pitches should be very close if not exact. If the regular fingering of the upper note is slightly sharp or flat small adjustments can be made by moving the mouthpiece on or off the cork slightly. Remember moving the mouthpiece on the cork and effectively changing the length of the saxophone has a greater effect on notes produced by a shorter tube than a longer tube because you are affecting a greater percentage of their wavelengths.
One of the intonation tests I like to perform on saxophones I am trying out is to play multiphonics (holding the note to sound both octaves simultaneously) fingering low Bb, B, and C and listening for "beats" created when the octaves are slightly out of tune. l hope my rambling helps your understanding a bit. If you have any more questions, please post them or send me a PM.
John