I understand what you are saying. But, because a ship is in a particular port, does not bring it under that command. There are only 2 fleets, Western and Eastern. There are no major surface combatants as part of Southern command. I have been to Kochi naval base, since thats my hometown and have seen the ships anchored there. There is an naval air station which falls under the Southern command. Southern command remains mainly a training command.
@Capt.Popeye will have a better understanding of this.