The kinetics of the disorder-to-order transition in a polystyrene-bloch-polyisoprene copolymer was studied after it was thermally quenched from the disordered state to the ordered state. The ordered state consists of cylinders arranged on a hexagonal lattice. This state has liquid crystalline symmetry with liquidlike disorder along the cylinders axis and crystalline order in the hexagonal plane. We monitor the kinetics of microstructure formation in the liquid and crystalline directions by a combination of time-resolved depolarized light scattering and small-angle X-ray scattering experiments. At small quench depths, microstructure formation along the liquid and crystalline directions is strongly correlated during all stages of the disorder-to-order transition. We demonstrate that this is expected when microstructure formation occurs by classical nucleation and growth. At large quench depths, however, microstructure formation along the liquid and crystalline directions is not correlated. The growth of crystalline order occurs before the development of a coherent structure along the liquid direction. We argue that this may be a signature of spinodal decomposition in liquid crystals.