The various transitions that can occur during thermosolutal convection in a saturated porous cavity filled with a Newtonian fluid are examined in this work in order to evaluate the effects of pores, solute concentration, and rotational force on this flow. To convert the linked equations into a six-dimensional system of nonlinear equations, we used a minimum-order double Fourier series method in line with Galerkin's truncated approximation. This resulting dynamical system is numerically solved using the fourth-order Runge Kutta method. The analytical computations are consolidated using phase spaces, time histories, bifurcation diagrams, and Lyapunov diagrams. The findings demonstrate the linear, chaotic, and period-doubling tendencies of fluid flow. In contrast to the situation of a Newtonian fluid, numerical computations have demonstrated that the existence of a solute concentration in a Newtonian fluid subjected to a rotational force postpones the onset of chaos and periodic convection. Numerical calculations demonstrate that various parameters such as porosity, solute concentration, and rotation significantly influence thermosolutal flow. These results have practical implications in several technical and geophysical applications, such as enhanced oil recovery, geothermal energy extraction, chemical reactors, and heat and mass transfer processes in porous media.