Please take note that we have not asked yet for rain. Bnei chutz lo’oretz only ask for rain in December and the bnei Eretz Yisroel ask on 7 of Chashvon.
All we did on Shmini Atzeres is hazkoras geshomim that HKBH is in charge of rain. We arent even akkowed to ask for anything until after the first three brochos of shmoino esrei.