As far as I know the definition of osmosis is a movement of solvent across a membrane, without extra energy input, so I don't think "salt osmotes into the cells

As far as I know the definition of osmosis is a movement of solvent across a membrane, without extra energy input, so I don't think "salt osmotes into the cells" makes sense. It would be diffusing along the gradient or undergoing active transport. I'm not a chemist, though.