This is an interesting issue as the Supreme Court has in several cases discussed the nature of the rights of nominees under various Statutes and has in the context of nominees of Insurance Policies, EPF accounts, Bank Accounts etc., held that a nominee would merely be an administrator (or custodian as you put it) and the property would not vest on him. However, in the context of Shares/Securities, a the Supreme Court in Aruna Oswal vs. Pankaj Oswal, (2020) 8 SCC 79 held that the securities vest on the nominee (i.e., the nominee becomes the owner).
Notwithstanding the above, one thing requires to be examined. On the basis of the information given by you, it seems like nomination was made for the Demat Account. There is a distinction between making a person a nominee of a Demat Account and making him a nominee of the Securities held in the Demat Account. This is an aspect that could be further studied and if found to be tenable, necessary steps could be taken for the transmission of the shares in accordance with the applicable law of succession.