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Referring to this, when "hydrolysis of a salt" is its reaction with water:
How is it that both the cation and anion of the salt are reacting in an equal amount with water?
To state this specifically in reference to the link provided, how is it that there is a unique $h$ (degree of hydrolysis)?
I think @ManishEarth has it right. The actual phenomenon involves not only the hydrolysis of the salt, but the autoionization of water. To keep things simple the autoionization of water in this case is often omitted in elementary textbooks.
In reality the hydrolysis of the anion and the cation are not normally identical and the resulting solution is slightly acidic or basic, depending on the nature of the ions.
Nevertheless, for each such reaction there is a definite amount of hydrolysis (which you call $h$ in the question). This constant will vary somewhat with temperature.
