I don't think that this has anything to do with Hindu conceptions of death. Rather, this is most likely a peculiarity of Indian English.
In many varieties of English, expire is a somewhat archaic, euphemistic synonym for "die". However, in Indian English, this is merely a euphemistic synonym for "die", not an archaic one. Some dude has put together an Indian English → British(?) English lexicon here that contains expire as an entry. While I don't know if the lexicon as a whole is useful, the fact that the creator chose to include expire further suggests that this is just another idiosyncrasy of Indian English.
This old version of the Wikipedia page on Indian English also lists "expire" as a a dialectal feature of Indian English. While the page is largely unsourced, it mostly jives with my intuitions as someone who has heard and read a fair bit of Indian English.
It is possible that the choice to use "expire" rather than a different euphemism like "pass away" is motivated by a conscious understanding of Hindu philosophy, but Occam's razor suggests that just isn't all that likely - this is probably another one of those nigh-inexplicable weird things about language.
EDIT: Amusingly enough, just earlier today, I talked with a not-that-religious Indian person who, completely unprompted, said "Did you hear about [so-and-so]? He expired."