Hi there, Welcome to Wikipedia! Thanks for improving the sentence in Shashi Tharoor. Your sentence does sound better than mine, certainly clearer. I don't often get an opportunity to discuss these things, so you'll pardon my little disquisition. Had I said, "Returning to India, he began schooling ..." it would have been an example of a (simple) participial clause, "Returning to India," (but) with adverbial meaning (i.e. it would tell us something about time). However, in "His parents returning to India, he began schooling ...," the participial clause has its own subject, "His parents," which is different from the subject of the sentence, "he." Such sentences are now considered formal. I did a Google search and most examples were a century old: see here!
There is a subtle difference in meaning, though, with "After his parents returned to India." It presupposes (in a way) that they were going to return to India. Let's say I had said instead, "His parents moving to South Pole, he began schooling at the Raol Amundsen Memorial High School." The sentence now does two things: it tells us a slightly surprising piece of information—that the parents moved to South Pole—and (when that happened) he began schooling at ..." Had we said, "After his parents moved to the South Pole, ..." or "When his parents moved to the South Pole, ..." we would imply that there was some inevitability (or something unsurprising) about that event, which, of course, there wasn't.