We investigated the dynamics of nanocomposites prepared through mixing poly(methyl methacrylate) grafted Fe3O4 nanoparticles (PMMA-g-Fe3O4) with poly(methyl acrylate) (PMA). A key feature here different from previous dynamics measurements of polymer nanocomposites is the different chemistry between the matrix polymer and the polymer grafts, which introduces chemical heterogeneity. Transmission electron microscopy shows clear evidence of nanoparticle clustering due to the poor miscibility between the bulk PMA and the bulk PMMA. At the same time, broadband dielectric spectroscopy measurements detect two leading relaxations, i.e. the alpha and alpha* processes, where the alpha process is associated with the bulk PMA and the alpha* process from the PMA interacting with the grafted PMMA in the nanoparticle clustering region. Interestingly, the characteristic time of alpha*, tau(alpha*), is slightly slower than that of the alpha, tau(alpha), at high temperatures, and exhibits near Arrhenius temperature dependence at low temperatures. As a result, tau(alpha*) and tau(alpha) cross each other in the activation plot upon cooling and tau(alpha*) << tau(alpha) is observed at temperatures approaching the glass transition temperature of PMA. These observations suggest the presence of component dynamics and the dynamics confinement effect between PMA and PMMA in the nanoparticle clustering region, highlighting an active interaction between PMA and PMMA at the interface despite their poor miscibility. These results thus suggest new routes to control interface dynamics through immiscible polymer pairs.