Why correlation property of $\mathcal Z$-transform contains a time reversal operation
Note that (discrete-time) convolution is defined as

$$x_1[n]\star x_2[n]=\sum_kx_1[k]x_2[n-k]\tag{1}$$

and correlation is defined as

$$r_{x_1,x_2}[n]=\sum_kx_1[k]x_2[k-n]\tag{2}$$

Comparing $(1)$ and $(2)$ we see that correlation can be written as the following convolution:

$$r_{x_1,x_2}[n]=x_1[n]\star x_2[-n]\tag{3}$$

The $\mathcal{Z}$-transform of $x_2[-n]$ is given by

$$\sum_nx_2[-n]z^{-n}=\sum_nx_2[n]z^n=X_2\left(\frac{1}{z}\right)\tag{4}$$

Consequently, from $(3)$ the $\mathcal{Z}$-transform of $r_{x_1,x_2}[n]$ must be

$$R_{x_1,x_2}(z)= X_1(z)X_2\left(\frac{1}{z}\right)\tag{5}$$