Proton spin–lattice relaxation, compressive strength, and water tightness measurements have been undertaken in order to study the hydration process and the mechanical properties of Portland cement modified with a calcium sulfoaluminate-based expansive additive (EXPAD). The compression strength of the modified cement was more than 70% higher while water permeability was about 60% smaller than in the unmodified cement. Magnetization–recovery curves analysis allowed for a time-resolved monitoring of both the increase of the internal surface as well as the formation of solid products during the hydration. A significant difference between the hydration kinetics of modified and unmodified cement was observed.