When the Southwest Monsoon arrives in India (June-September), it comes in two branches:
The Arabian Sea branch - which brings heavy rainfall to the western coast
The Bay of Bengal branch - which brings rainfall to northeastern India and then moves westward
Tamil Nadu remains relatively dry during this period because:
The Western Ghats act as a barrier to the Arabian Sea branch of the monsoon
The moisture-laden winds from the Arabian Sea release most of their rainfall on the western side of the Western Ghats (Kerala, western Karnataka)
By the time these winds reach Tamil Nadu, they have lost most of their moisture
This creates a "rain shadow effect" on the eastern side where Tamil Nadu is located