Why effigies of Ravana are burnt down in October - November ?

In many parts of India, we can view burning of effigies of Ravana, Indrajit and Kumbhakarna during the Dussera/Deepavali period.

The vanaras sent in Southern direction in Sarad Ritu (September - October) lose their way and enters in a Big cave and finally reach a big mansion.  After coming out of that cave and reaching Ocean, they found that much time was lost and already Vasanta Ritu - Spring season (March -Arpil)  has arrived.

ते वसंतम् अनुप्राप्तम् प्रतिवेद्य परस्परम् |
नष्ट संदेश काल अर्था निपेतुर् धरणी तले || ४-५३-५

"On discussing among themselves they found that spring season has arrived, and they also found the purpose of timely messaging about Seetha to Sugreeva is lost, thus they plumped down onto the surface of earth"


Sri Hanuma reached Lanka during the Vasanta Ritu (March-April).  If we add one month, for Sri Rama travelling and reaching and eliminating Ravana, after a bitter fight, it will Chitra or at the most Vaishakha month (April-May).

So if at all the victory of Sri Rama over Ravana has to celebrated it should be in the Vasanta Ritu or Grishma Ritu but not in Sarad Ritu (September-October).