To enhance the thermal stability of new experimental cast Mg—10.5Al—0.4Ca—0.3Mn—0.2Ti alloy, the kinetics of decomposition of its solid solution (in the as cast and supersaturated states) is investigated with an activation analysis of quenched states in the temperature range of 673—293 K. The decomposition kinetics of the multicomponent alloy obeys the Cottrell—Bilby law, and the thermal stabilization process is controlled by the activation of Cottrell—Bilby and Avrami—Harper dislocation mechanisms, which connect long-range diffusion of the refractory alloying elements to unpinned dislocations with short-range saturation of the Cottrell atmospheres and formation of nanosized phases at dislocations. Additional electrohydropulse processing (EHPP) of the liquid alloy changes the kinetics of decomposition, inhibits short-range separation of the $\alpha$-Mg solid solution, and it stimulates the formation of clustered regions, which are thermally stable up to 693 K. According to the resistivity and X-ray diffractometry, it is revealed that, after EHPP, thermal stabilization of the primary $\alpha$-Mg solid solution is achieved through clustering of its structure to form pair defects, i.e., primary clusters of Al—Ti. Because of the complex heat treatment, the thermal stability of the alloy is increased to 523 K. The increase in the volume of $\beta$-Mg$_{17}$(Al, Х)$_{12}$ fraction enhances the beneficial effect of its dispersion hardening.