He was born in India - the event of his birth happened in India, some years ago.
He is born in India - he is today a person who was born in India. Yesterday, he was also a person who was born in India, and he tomorrow he will also be a person born in India. But we are talking about today, so he is born in India. You might say "He is India born". You often hear "he is Oxford educated". "He is India born" would mean that this isn't just the place where he happened to be born, but that it is of importance to describe him today.
You use the past tense if you are talking about events that happened in the past. You can use the present tense if you are talking about the past events making him the person that he is today. "I am born in India" does that. "I am born at the hospital near my parents' home" - that would be wrong, because that event doesn't describe the person you are today. Or "I am born in India, but my parents moved to China two weeks after my birth" - I'd assume that two weeks in India didn't have much influence on the person, so I'd use "I was born... " in that case.
You may also search for the lyrics of "Born in the USA" by Bruce Springsteen. Apart from finding some "interesting" words, you'll also see the line "I'm born in the US of A".