I don't have much idea but from what i know, BMD is operated by IAF as its IAF responsibility to protect indian airspace from hostile entity.
But it will surely change, IN will have BMD on their destroyers within a decade and may be as well around naval base.
SFC only operates land+air nuclear missiles and warhead.
I guess SLBM is in command of IN but may be they need SFC confirmation(codes) to launch it.