This paper discusses the phenomenon of evolving spherically symmetric cluster of stars in the presence of an exotic matter. To discuss evolutionary mechanism, we use the Starobinsky model of f(R) gravity as exotic matter and the structure scalars as evolutional parameters. We study various evolution modes such as isotropic pressure, quasi-homologous evolution, density homogeneity, and geodesic nature. The stability of homogeneous density of baryonic and non-baryonic matter is discussed using dissipation, tidal forces, anisotropic pressures, expansion and shear-effects. It is observed that the dark matter has remarkable impact on the evolutionary changes. Also, it is shown that the dissipation factor produces density inhomogeneity in expanding clusters with shear effects. We observe that high curvature geometry enhances quasi-homologous evolution in the presence of shear. We use star Her X-1 as test star to discuss physical behavior of Starobinsky model. It is found that the density of dark matter overcomes the density of matter for large values of dark matter parameter n.