thx for brining this up.
This is a genuine concern (

) ): what do we actually see when we look at the moonphase of our calendar.
I follow your reasoning. a step is a step and between 2 steps, well, nothing changes. Whic means the display when sync properly displays the real thing only at the time of the next step.
I was under the impression though, that in the case of the Atmos, the moonphase indicator is directly and "constantly" (if it means anything for a clock that receives an impulsion of energy every 30s) driven by the calibre hence the moon indicator is constantly displaying the moonphase by increments of 30s (each beat of the clock). So, if everything is set right at some point, when you look at the moonphase you see it displayed with a 30s accuracy compared to the real phenomenon.
Considering that the moonphase is averaged with a cumulative error of 3s per moon cycle, it will take 10 moon cycles before this cumulative error is bigger than 1 beat. So almost a year with almost perfect moon phase display. (not considering that the clock itself will run a little bit fast or slow over that same period and this would impact the whole system far more, as a couple of seconds per day will turn into a couple of minutes per month... but here you go, this is watchmaking, for mere mortals

)
I find it funny that it is quite a challenge to quantify the accuracy of such poetic complication as the moonphase display in various calibres.
I enjoy the logic behind it because I find it incredible to be able to have a mechanical device that represents the position of Earth, Moon and Sun right in front of me.
I think there is also room for new complications displaying or allowing to accurately sync the moonphase on a watch or a clock.
One can hope to be heard by the watchmaking brand we are passionate about.