The Sidereal traditions correct for the precession, the Tropical ones are frozen and increasingly out of sync. Tropical is the majority tradition among westerners. The big tradition in India, Jyotish, is Sidereal, but mainstream Jyotish doesn't acknowledge planets beyond Saturn, the ones that needed a telescope to be discovered.

I, uh, tried a lot of things in the long years before I found Marx.

Well, so like, there are the constellations that the signs are based on, but there's also the segments the year is cut into with the same names. I assumed they were still (at least mostly) in line with the calendar, unless they had to inscribe a new astrolabe every year which isn't impossible. So the full moon aligning with the Capricorn constellation during the 29th degree of Capricorn, which I'll assumed she got the date right; I don't have an astrolabe on hand. EDIT: I think they misread, it appears to be the 29⁰ of Cancer, but maybe location has something to do with it?