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
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.