The spin dynamics in a broad range of systems can be studied using circularly polarized optical excitation with alternating helicity. The dependence of spin polarization on the frequency of helicity alternation, known as the spin inertia effect, is used here to study the spin dynamics in singly charged (In,Ga)As/GaAs quantum dots (QDs), providing insight into spin generation and accumulation processes. We demonstrate that the dependence of spin polarization in n- and p-type QDs on the external magnetic field has a characteristic V- and M-like shape, respectively. This difference is related to different microscopic mechanisms of the resident carriers' spin orientation. It allows us to determine the parameters of the spin dynamics both for the ground and excited states of singly charged QDs.