When does the 12-month extension on a Non-O visa start after applying in Thailand?

when you enter, you get stamped in for a 90-days stay permit. The Non-O Visa will become invalid. Then before this stay permit expires, you apply for the 1-year extension of the stay permit (based on reason retirement). The 1-year extended stay permit will begin on the day AFTER your initial 90-days stay permit expires

👆👆👆 for a total of 15 months

It's an extension. It extends your time. It's added on to the end because the extension you'll be applying for will be for the reason as the entry stamp you receive.