We have studied adsorption of nonadditive binary symmetric hard sphere mixtures in hard sphere matrices and in templated hard sphere matrices. Adsorption is described by using replica Ornstein-Zernike integral equations complemented by Martynov-Sarkisov closure relations. This theory permits straightforward calculation of the chemical potential of fluid species and to describe equilibrium between the bulk phase in a model adsorbent body. Theoretical results for adsorption isotherms agree well with Monte Carlo computer simulation data. On the other hand, we have captured the effect of matrix modification on adsorption via templating. Finally, we have described the coexistence curve (in terms of concentration vs density and in terms of concentration vs chemical potentials of fluid species) for the demixing transition by using theoretical procedure and by semigrand computer simulation in hard sphere matrices and in corresponding templated matrices. We have shown that the explanation of the phase behavior is intrinsically related to the trends of adsorption of the model fluid in such disordered adsorbents.