Why does it rain more at night than during the day?
First off, your observation that Tamil Nadu gets more rainfall in the evening is partially backed by records. Sahany, Venugopal, and Nanjundiah, 2010 provide data on diurnal scale rainfall distribution during the Southwest monsoon season shows that Tamil Nadu is dry from 0530-1430 each day, and likely to be wet from 1730-0230:



The Northeast monsoon is different. From Rajeevan et al, 2012 the NEMR (North East Monsoon Rainfall) peaks in the evening for most of Tamil Nadu but the coast facing the Bay of Bengal (including Chennai) peaks in early morning (0330-0630):



Regarding the reasons for this, here are some excerpts from Basu, 2007:


  In the Tropics most of the rainfall is from the tall clouds (Cu or Cb)
  formed by convection within a deep layer of the atmosphere. The usual
  forcing for such clouds to form is the heating from below by the solar
  radiation absorbed by the ground during the day. This forcing is
  maximum near the time of maximum surface temperature and the first of
  the thunderstorms caused by insolation start near 1430 local time


and 


  Over the sea areas along the east coast (south of 15°N) too, the
  maximum in precipitation occurs in the early morning hours as the
  synoptic-scale westerly is weak over this region and the diurnal
  variation is dominated by the land–sea breeze.


Also worth noting, from Roy and Balling, 2007:


  The strength  of  the  diurnal  cycle  is  greatest  in  the 
  peninsular region with close to 96% variance explained for stations
  located in Tamil Nadu.


My interpretation of this is that inland Tamil Nadu sees high surface temperatures from sunlight through clear skies striking the ground. The resulting heat is released in the late afternoon and evening, which causes cumulus or cumulonimbus cloud formation and rainfall. During this, the ground cools off at a rate faster than the nearby Bay of Bengal. This causes oncoming sea breezes laden with moisture and coastal rainfall peaks in the early morning hours. In Tamil Nadu especially, this pattern is very stable.