@misterthomnus if you're here as a tourist only, then the information discussed in the Lovely Blue article is what you'd go by. You can go to this website (
https://www.migraciones.gov.ar/transitos/) and verify when your current 90-day period expires. For example, my last return trip from Colonia was on November 30th, so my current 90-day period expires on February 28th. If I want to extend it officially, then I need to go to the Migraciones office no more than 10 days before the period expires (i.e. sometime between February 18th and 28th). In my case I have another Colonia trip planned at the end of January which will reset my clock. You can only receive one extension as a tourist before you either have to leave the country again or overstay and pay the fines.
Tourist travel plans change all the time, which is why they make you wait until 10 days before your time expires so they don't end up granting lots of unnecessary extensions that never get used. Colombia also had the same "no more than 10 days prior" rule for tourist extensions when I was there as well.
The information you found on the Migraciones website regarding extensions of "residence" is (I presume) referring to those who have formalized their status here by way of temporary or permanent residency and who are looking to extend their residency or change their residency status. If you're just here as a tourist, then your only two option as I understand it are to either request an extension in-person (no more than 10 days in advance of when you need it), or to make another trip to Colonia, Santiago, etc.