I don't think I blow any spit into my sax. I collect it in a space under my tongue, behind my lower front teeth, and swallow it when time permits.
If the player plays leaning forward, or with the head down, then this 'pool' of spit can easily enter the sax. So, head up!
If this is indeed, just condensation, then also attend to what you do with the sax during rests. You may be tilting the sax so that the condensation runs to these tone holes.
Warning: The rest of this post is gross! But so might be your sax.....
"As Hakukani and others have pointed out it's not spit, or "spittle!" It is water (H2O) condensed out of the warm air from your lungs. "
Yes, that is an ideal. But in reality, it is naive.
Every experienced technician must have met saxes which have a gooey, off-white lining (of shed mouth cells?), inside the bore of the sax, especially in the upper half. Sometimes it can be 1/2 to 1 mm thick if the player does not swab the sax for a long. It's gross; it's 'reach-worthy'. It is semi-dried spit from a food-ridden or unhealthy mouth. Much more often, the neck is lined with the stuff, probably because more people don't clean necks. Also the dried equivalent is often seen flaking off inside the lower end of the sax, where it has more chance to dry.
This is not a product of condensation! To me, it is obvious evidence that quite a lot of players do indeed blow a fair bit of spit into their sax.
I have also seen saxes with that dried stuff all over the mechanism. One player explained that he was a 'wet blower'. What he meant was that this was the dried residue of what came out of the sides of his lips while playing, or possibly even from his nose. Charming! Student Yamahas have the most amazingly robust lacquer, but the that two-year-old sax had probably the most corroded keywork I have ever seen.