Understanding the molecular structure of the hydration shells and their impact on the hydrogen bond (HB) network of water in aqueous salt solutions is a fundamentally important and technically relevant question. In the present work, such hydration effects were studied for a series of representative salt solutions (NaCl, KCI, CaCl2, MgCl2, and KBr) by soft X-ray emission spectroscopy (XES) and resonant inelastic soft X-ray scattering (RIXS). The oxygen K-edge XES spectra could be described with three components, attributed to initial state HB configurations in pure water, water molecules that have undergone an ultrafast dissociation initiated by the X-ray excitation, and water molecules in contact with salt ions. The behavior of the individual components, as well as the spectral shape of the latter component, has been analyzed in detail. In view of the role of ions in such effects as protein denaturation (i.e., the Hofmeister series), we discuss the ion-specific nature of the hydration shells and find that the results point to a predominant role of anions as compared to cations. Furthermore, we observe a concentration-dependent suppression of ultrafast dissociation in all salt solutions, associated with a significant distortion of intact HB configurations of water molecules facilitating such a dissociation.