New York bank has no power to instruct the bank at Pune to settle the amount to the nominee upon the death of the account holder.
However, as per RBI instructions, Banks are advised to settle the claims in respect of deceased depositors and release payments to survivor(s) / nominee(s) within a period not exceeding 15 days from the date of receipt of the claim subject to the production of proof of death of the depositor and suitable identification of the claim(s), to the bank's satisfaction.
The benefit of nomination is that in the event of death of an account or locker holder, the bank can release the money in the account or contents of the locker to the appointed nominee and won't insist on other documents like succession certificate or a legal heir document.