In chapter 10, sloka 12 of Sri Sri Chandi, devi says :
शरत्काले महापूजा क्रियते या च वार्षिकी
meaning that in the sarat (autumn) seaon, my great annual puja is done. So in the very Chandi, Sri Sri Durga recognizes the saratkaalin durga puja.
Then why is it told that Rama worshipped Her first in an inappropriate time (Akala)? Chandi is from Swarochisha mannantwara by the way.