It's true that those MySQL data types don't contain a time zone. But the MySQL server has a time zone, and that's the time zone it will use to interpret the data types.
You should run your application with the same time zone, otherwise bad stuff is going to happen.
(Both MySQL and your application will get their time zone from the system they are running in, although it's probably possible to override either. I'd advise just running them both in IST, in fact you're probably already doing that.)