Does water volume decrease when salt is added to it?

The absolute volume increases monotonically from pure water to halite saturation but it does not necessarily increase by the volume of the salt added to the water. At low salt concentrations the dissociation of the salt causes a contraction of water molecules around the ions; thus the reason for the lack of strict additivity. As salt concentration increases the contraction effect decreases.

If you've heard someone talk about the volume of a salt solution decreasing relative to pure water what was probably referred to as “specific volume” which is the inverse of density. As NaCl is added to water the density of the solution increases so the specific volume decreases.

And just to confuse you: apparent molar volume is a measure of a solution’s volume relative to the solvent volume weighted by the number of moles of solute. That volumetric measure can be greater than, equal to, or less than the infinitely dilute solution depending on the specific salt, the concentration of salt, temperature, and pressure.