Why autumn follows the rainy season
The precise reasons for leaf shedding after monsoon aren't well known and studied, but there are vague reasons like optimising use of light and warmth for max photosynthetic gain. So the tree has a heavy load of leaves to grow fast in monsoon, and it fast depletes the groundwater if it keeps the leaves in the dry season. read the conclusion here: https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1466-8238.2006.00213.x
Trees need to store reserves to allow their survival during winter and for bud flush and leaf growth in the following spring.
Generally it takes 2 weeks or a month for a deciduous tree to prepare dormancy/sleep time, to gather all the nitrogen, glucose and nutritive elements from their leaves.
If the plant keeps on growing when it's leaves are adapted to massive rainfall, it may lose the green leaves rather than gather useful elements and prepare for dormancy.
i.e. from this image you can see the winter stored sugar being used to grow new leaves, for this tree the spring is in april: 
There's some interesting facts about leaves here: https://en.wikipedia.org/wiki/Autumn_leaf_color#Function_of_autumn_colors