Exploring the ordering mechanism and dynamics of self-assembled block copolymer (BCP) thin films under confined conditions are highly essential in the application of BCP lithography. In this study, it is aimed to examine the self-assembling mechanism and kinetics of silicon-containing 3-arm star-block copolymer composed of polystyrene (PS) and poly(dimethylsiloxane) blocks as nanostructured thin films with perpendicular cylinders and controlled lateral ordering by directed self-assembly using topographically patterned substrates. The ordering process of the star-block copolymer within fabricated topographic patterns with PS-functionalized sidewall can be carried out through the type of secondary (i.e., heterogeneous) nucleation for microphase separation initiated from the edge and/or corner of the topographic patterns, and directed to grow as well-ordered hexagonally packed perpendicular cylinders. The growth rate for the confined microphase separation is highly dependent upon the dimension and also the geometric texture of the preformed pattern. Fast self-assembly for ordering of BCP thin film can be achieved by lowering the confinement dimension and also increasing the concern number of the preformed pattern, providing a new strategy for the design of BCP lithography from the integration of top-down and bottom-up approaches.