The aims of the arts are to make the ink follower follow the ink smoothly.
I imagine they've made it viscous/non-Newtonian/whatever (not sure on the technical fluid mechanics term) enough such that gravity pushes/pulls it down towards the tip but prevents it from flowing the other way.
Edit 1 (just before getting in the shower): Removed references to air pressure, as I don't think that makes a difference.
Edit 2 (post shower): Air pressure might a difference after all, it depends on where the seal is. If there's an air tight seal on the tip end (which there might be, if that's how it's kept from leaking) then air pressure might add to the "only goes one direction" effect.