If you somehow made a spherical hole in the middle of the earth and placed a cup of water inside the hollow (anywhere inside, doesn't have to be the centre) it will just sit there: Newtonian gravity is 0 inside a uniform spherical shell of mass. (Einsteinian gravity is probably mostly 0 but you'll get frame dragging effects if the shell is rotating I would imagine.)
You can do the maths to prove this yourself if you want.
In the ISS the air pressure is artificially kept at a certain level. To make a proper comparison, you should check what water would do outside of the ISS.
The context of my original comment was someone expecting that a cup of water at the centre of the earth would explode due directly to gravitational effects. This is wrong, as I pointed out.
Even on the surface of the earth it is the air pressure that prevents the water boiling off instantly, not gravity itself. On the surface of the earth that air pressure is due to the effect of gravity on the atmosphere, but you can supply that air pressure by a number of other means in other places. The air pressure inside the ISS is not there due to gravity after all! I suggest to you that if we can posit a hole at the centre of the earth, then we can fill it with air at 1atm if we want to - we are in the realm of mathematical models here, not reality after all :)