Wow – that’s one I’ve never heard – about rubbing tumeric powder on the skin to remove hair. I love tumeric to cook with but I really wouldn’t advise rubbing it on your skin because it will stain it. That sounds like exactly what happened.
Basically it should come off within a couple of weeks as it’s just the cells of the outer dead layer (stratum corneum) that are stained. Please do NOT over scrub this trying to get it off. It will cause irritation which could cause more pigment to develop.
Just very gently use a wash cloth on it every 2-3 days and it should gradually lighten. If it doesn’t, see a dermatologist please.