The crystallization kinetics of poly(ethylene oxide) (PEO) blocks in poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB)/poly(1.4-butadiene) (PB) blends were previously found to display a one-to-one correlation with the microdomain morphology. The distinct correlation was postulated to stem from the homogeneous nucleation-controlled crystallization in the cylindrical and spherical PEO microdomains, where there existed a direct proportionality between the nucleation rate and the individual domain volume. This criterion was valid for confined crystallization in which the crystallization was spatially restricted within the individual domains. However, it was possibly not applicable to PEO-b-PB/PB, in that the melt mesophase was strongly perturbed upon crystallization. Therefore, it may be speculated that the crystal growth front developed in a given microdomain could intrude into the nearby noncrystalline domains, yielding the condition of cooperative crystallization. To establish an unambiguous model system for verifying the existence of microdomain-tailored kinetics in confined crystallization, we crosslinked amorphous PB blocks in PEO-b-PB/PB with a photoinitiated crosslinking reaction to effectively suppress the cooperative crystallization. Small-angle X-ray scattering revealed that, in contrast to the noncrosslinked systems, the pre-existing domain morphology in the melt was retained upon crystallization. The crystallization kinetics in the crosslinked system also exhibited a parallel transition with the morphological transformation, thereby verifying the existence of microdomain-tailored kinetics in the confined crystallization of block copolymers. Homogeneous nucleation-controlled crystallizations in cylindrical and spherical morphologies were demonstrated in an isothermal crystallization study in which the corresponding crystallinity developments followed a simple exponential rule not prescribed by conventional spherulitic crystallization. Despite the effective confinement imposed by the crosslinked PB phase, crystallization in the lamellar phase still proceeded through a mechanism analogous to the spherulitic crystallization of homopolymers.