I would assume the sun isn't counted as a star, since it isn't in 'real' Western astrology which they seem to be using as a basis. The sun and moon are grouped with the planets, being moving objects against the 'fixed' stars.
I have to wonder if, while an astrologian's magic skills are real enough, the fortune-telling elements might not be a necessary part of their abilities but just 'tangled up in it', a bit like real-world alchemists developing knowledge of real chemistry while mixing it with a great deal of superstitions and beliefs that don't actually have anything to do with the chemical processes. Or the science of astronomy within astrology itself.
(After all, they're running their calculations to include a moon that is no longer there and actually wasn't a real moon in the first place. Clearly it's not making a lot of difference to the practical outcome of their answers, even if they believe it is.)
It's even possible the 'functional' part of astrologian magic isn't really drawing aether from the stars at all, the caster simply thinks they are, and they're actually drawing ambient aether from the air or something.
Suppose the core working concept of what they do is actually something like arcanistry. The patterned constellations on their star globe - or in the sky itself - might act in the same way as an arcanist's geometric patterns, and their spells cast in the same way. (Both weapons use enchanted ink in their construction, described in the Lv20 alchemist quest as being conductive to aether and "the most important aspect of any grimoire".)
Interestingly, having had that thought, I realised that arcanistry (via scholar) is also a healing discipline with sun and moon elements! But does it all line up?
Eos (sun faerie) has Regen, magic-defence boost and healing boost spells.
Selene (moon faerie) has Silence, Esuna and speed boost spells.
Eos having Regen even lines up with Diurnal Sect's aspected spells, though Selene doesn't match up so well, since it's the scholar themself that uses the shielding spells.
Something to think about...