Yes, I am aware that Queen Victoria assumed the Imperial style after the Colonial Office took over the administration of India. But it was a colonialist affectation and the House was never styled "of India".
The extent to which Indians, themselves, regarded the House of Safe-Coburg Gotha/Windsor as being "of India" can be gauged by the alacrity with which India declared itself a republic.
Wasn't India a Kingdom for a short period after gaining independence?