I wonder if we are confusing the terminology here? When you use the term "precaria" are you really referring to a precaria, or in infact to a temporary residency?
If all you did in September 2020 was successfully lodge the documentation they require for an applicant for a residency as a pensioner, then the document they issued you (and that you have kept renewing every three months) is a precaria that you hold until such time as they (i) grant you residency as a pensioner, or (ii) ask you for more information to help them assess your application, or (iii) deny your application. That may be the situation you have been in all this time: holding a precaria while they consider your application. In that case, you do need to stay in the country 183 days from the issue of the precaria (and you may--depending on the pandemic rules--need to be in the country at each point your seek your 90-day renewal). They will not issue you with a DNI at that point. If, in the future, they approve your application for temporary residency as a pensioner, only then can you apply for the DNI. And it will be at that point that your initial question (what date counts for the 365-day countdown?) come into play.
If, on the other hand, in September 2020 they granted you a 12-month temporary residency as a pensioner (you having previously lodged all the documentation and having been issued 90-day renewable precarias while they considered your case), then you are indeed a 12-month temporary resident, you have completed 183-days in Argentina in the first 365 days (since September 2020), and you now need to apply for another 12-month temporary residency in time for September 2021. (And, if you are not from a Mercosur country, you will need to repeat this process one more time--in 2022--in order to become eligible to then apply for permanent residency).
Which is it, do you think? Do you (i) have a precaria granted in Sept 2020 while they assess your application for temporary residency, or do you (ii) have temporary residency that was granted in Sept 2020 on the basis of an application you lodged prior to Sept 2020.