Dynamic scaling laws derivation

In the book Critical Dynamics by Tauber the following scaling hypotheses are made for the static correlation function and for the characteristic frequency in Fourier space
$$
C(tau, q) = |q|^{-2+eta} hat{C}_{pm}(q xi)
$$
$$
omega_{c}(tau, q) = |q|^z hat{C}_{pm}(q xi)
$$
Here $tau$ is the reduced temperature and $xi$ is the correlation length.
Then at page 99 the following dynamic response function
$$
chi(tau,q,omega) = |q|^{-2+eta} hat{chi}_{pm}(q xi, omega xi^z/Da_0)
$$
where $D$ and $a_0$ are some "microscopic time and length scales". This response function is introduced as a natural consequence of the previous statements but I have not understood what is the logic behind this generalized scaling hypothesis. I mean, on the basis of which hypotheses should this response function be written in this way?