India mandated TCAS on all aircraft in its airspace after the terrible 9Y/SV collision over DEL in 1996. Its alerts the crew of all involved aircraft about to breach the separation minimums of impending 'doom' and advises which corrective action each should take.

What you witnessed was a standard encounter. The airspace over India is very crowded and all follow invisible 'highway' corridors. If you can post the flight you took, I can look up a routing your flight probably took and where the turn is required.