We demonstrate that the morphological diversity in liquid-crystal hybrid systems is much richer than previously anticipated. More importantly, we reveal the existence of a dual mechanism for self-assembly of nanoparticles via morphological instabilities at phase boundaries. Using numerical simulations, we study the growth of isolated nematic droplets in an isotropic liquid crystal (LC) doped with nanoparticles (NPs) and provide insight into the nature of microstructure evolution in LC hybrids. Our work expands the numerically accessible time and length scales in these systems, capturing morphologies which develop under the competition of nonequilibrium elastic interactions, diffusive instabilities mediated by NP transport, and the anisotropy of the nematic field. By mapping nematic morphologies, we also propose a methodology for estimating various important LC material parameters that are difficult to obtain experimentally.