Pressure and compressibility are two separate concepts.
It is possible to vary the pressure without reducing the volume of a substance.
Imagine an anvil.
Put a 10lb barbell on it. This exerts a pressure, but did you change the volume of the anvil? Probably, but not by any measurable amount.
Put a second 90lb barbell on top of the 10lb barbell. You now have 10 times the pressure of just the 10lb barbell. Did the anvil change volume? Same answer.
Sound is not a wave of fluctuating densities, it is a wave of fluctuating pressures.
And as an aside, we say water is incompressible, not because you cannot compress it, but that it undergoes such minimal compression that we can almost always ignore any compression that occurs.
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