How do you access the locked area in Poseidon Plaza? [duplicate]

I've been playing through Bioshock again, and there's an area in Poseidon Plaza which I can't figure out how to get to.

This is the place on the map:
click to enlarge

This seems to be the (locked) entrance to it:
click to enlarge

How do I get in there?

1. Go into Sinclair Spirits (left to the view on the second screenshot).

2. Find the switch behind the counter and use it.

   

3. A door on the wall opposite to the counter will open.

   

   Go through that door and go downstairs, where you will find a Power to the People machine. Use this machine.

4. After returning upstairs, the previously locked stairwell will be unlocked.