Strictly speaking, it is not that the constellations move around us, it is that our Sun, and hence we, are moving around the Milky Way galaxy, and in turn the Milky Way galaxy has movement relative to its galaxy cluster, and that cluster has relative movement to the rest of the cosmos. Add to that the slow wobble of the Earth about its axis and the resultant perception of terrestrial observers is the precession of the 12 houses of Astrology.
None of this is precise if measured from the perspective of an observer on Earth. Hence, various people at various times have estimated the cycle around the Zodiac to be anywhere from 24,000 to 26,000 years. The best explanation may be the one involving the Sun moving in concert with its binary twin. Again referring back to Kepler's laws, that would mean the perceived precession of the constellations is not a constant speed, but rather a speed which speeds up and slows down dependent of where we are on the elliptical path. Which is to say that neither sidereal or 'western' astrology is perfectly accurate.
What is most relevant is that, how ever long it takes, at whatever speed we are moving at any particular point, our relative position to the constellations changes and, per the core of astro-whatever science, this translates to some as yet not perfectly defined change in the events of men.
And it is 100% based on science, despite the disbelief of some that astrology is foolish superstition. It is a scientific fact that a woman's menstrual cycle is affected by her relative position to the moon. Ditto for the tides going in and out. What mainstream science is reluctant to seriously measure is the effect of cosmic movement upon Consciousness.
Instead, we are frequently assured that far away stars are too distant to be having any significant effect of us. But, how can mainstream science, really, be sure of that? The mere reality that scientists do not, really, know exactly what dark matter [most of the cosmos] is, other than it is everywhere, has to mean that there is much about our relationship to the cosmos that science is not cognizant enough of to write off Astrology as myth and fable.