ज्योतिषे विश्वासटिप्पन्यः

The ayanAMsha used to determine nakShatra or lunar month in a particular ritual context should be determined from the vidhi-vAkya-s enjoining that particular ritual action.

Apastamba example

Take upAkarma. Apastamba says: “(आर्तव)श्रवणा(पूर्व)पक्ष ओषधीषु जातासु हस्तेन पौर्णमास्यां वा ऽध्यायोपाकर्म २”. So, when do saplings sprout? At the beginning of the (khArif) rainy season, around the summer solstice time in north India. This happened to be shrAvaNa around 1000BCE. The crops don’t srout when xyz-ayanAMsha based month happens to be “shrAvaNa”. That’s when adhyAya-upAkarma should be celebrated. Effectively, the naxatra-chakra should be “tropicalized” so that shrAvaNa pUrNimA falls around the time of solstice. People who claim to follow Apastamba by celebrating sometime in August are the same sort of comedians (unwitting or otherwise) who would “show” arundhati at noon during faux-vivAha rituals.
Then take sarpabali. Apastamba says: “श्रावण्यां पौर्णमास्यामस्तमिते स्थालीपाकः ५ … मार्गशीर्ष्यां पौर्णमास्यामस्तमिते स्थालीपाकः ३”, and recommends giving bali to sarpa-s between shrAvaNa pUrNimA and mArgashIrSha pUrNimA. The timing is again tuned to nature - rainy season is when snakes come out of their flooded homes, and incidence of snake bites increase. So, again, anyone more interested in the spirit as well as letter of the AchArya will offset the naxatra-chakra so that shrAvaNa falls around solstice time - yes, tropicalization again. It is again comical if people keep giving bali-s in December. (Of course, people can start saying that “sarpa-s” are not snakes and that it is some “yoga” to be out of sync with nature - but they’re welcome to their private universe.)

वायुपुराणोदाहरणम्

For example, vAyupurANa says: मेषान्ते च तुलान्ते च भास्करोदयतः स्मृताः । मुहूर्त्ता दश पञ्चैव अहोरात्रिश्च तावती ।। ५०.१९५ ।। कृत्तिकानां यदा सूर्यः प्रथमांशगतो भवेत् । विशाखानां तथा ज्ञेयश्चतुर्थांशे निशाकरः।। ५०.१९६ ।। विशाखायां यदा सूर्यश् चरतेंऽशं तृतीयकम्। तदा चन्द्रं विजानीयात् कृत्तिकाशिरसि स्थितम् ।। ५०.१९७ ।। विषुवन्तं तदा विद्याद् एवम् आहुर् महर्षयः। सूर्येण विषुवं विद्यात् कालं सोमेन लक्षयेत् ।। ५०.१९८ ।। The second half of the first verse clearly tells us that during equinox, it is expected that both day and night are of equal length (15 muhUrta-s).
The remainder goes on to tell us how the exact timing for the sadAchAra conduct described in succeeding verses are to be timed: A careful ritualist should first adjust ayanAmsha so that the sun at equinox appears in kRttikA as described, and then optionally (if one intends to emphasize lunar position more than day-night equality) await the time around the equinox day when (~full) moon is in vishAkhA (as per this ayanAMsha adjustment). This of course results in shifting the naxatras from the corresponding asterisms (eg. Pleiades).
This choice of ayanAMsha incidentally corresponds to the ritual requirements of yajurveda portions (such as the puNyanaxatra section of taittirIya brAhmaNa).
Instead of this, if starts off with some other ayanAMsha from some other context and goes then to deduce “equinox” based on it - that would be wrong-headed - like latching the horses behind the cart.