You are fine tuning the distance (and adjusting the tension as well) of the standing wave, and in essence moving the exact middle of the wave over the 12th fret.
You can tune a string over a broad (relatively speaking) range of distances on the bass, which moves the midpoint around. Intonation puts it where it belongs.
Each string, being under different tension and having different mass (diameter) behaves differently, thus, the saddles will be in different positions.
Take an 105 gauge E string off and put on a 100.
Pretend we can do this without touching the tuner.
It would be out of tune, so, retune, tension is changed, so that midpoint has also moved a little.
I just set up my fretless and was amazed at how little distance is needed off the line to throw off intonation setup. It only seems like we move the saddle really far, but remember you are retuning after moving it, compensating for tension changes etc.
It’s hard to visualize because you have mass, distance and tension at play.