Chloride ingress, along with chemical and physical binding in cement pastes, was studied in relation to the paste composition, saline solution, and hydration regime used. Unblended cement paste and pastes prepared with combinations of SF with MK and SF with BFS, replacing 30% of the cement mass, were exposed to NaCl and geothermal solutions for 7 days, either directly or following 7 days of water curing. The surface and middle parts of the samples were evaluated using TGA, XRD, FTIR, ion chromatography (Cl concentration), and ICP-OES (Na concentration). In addition, compressive strength (CS) measurements were performed. In MK-containing samples, Cl-AFm (hydrocalumite) formed mainly through an ion exchange mechanism, while in BFS-containing samples and the reference pastes, Cl-AFm phases primarily formed through the reaction of Cl− with C3A and Ca(OH)2 and increased physical adsorption of Cl− onto C-(A-)S-H were determined. Exposure to NaCl solution led to more chlorides being chemically incorporated into Cl-AFm, as well as higher levels of physically adsorbed and free chlorides in the pore solutions, compared to the geothermal solution. Pozzolanic reactions of additives, the acceleration of hydration induced by the solutions, especially by the geothermal one, and the densification of the matrix by the products of chloride reactions in blended samples resulted in CSs comparable to or higher than those reached after standard water curing. CSs of referential samples decreased following the decalcification of the initially formed C-(A-)S-H phases.