The Nd0.6Sr0.4MnO3 manganite system exhibits a phase transition from paramagnetic insulating (PMI) to ferromagnetic metallic (FMM) state around its Curie temperature TC = 270 K (bulk). The morphology-driven changes in the kinetically arrested magnetic phases in NSMO thin films with granular and a crossed-nano-rod-type morphology are studied. At low temperatures, the manganite thin films possess a magnetic glassy state arising from the coexistence of the high-temperature PMI phase and the low-temperature FMM phase. The extent of kinetic arrest and its relaxation was studied using the "cooling and heating in unequal field (CHUF)" protocol in magnetic and magneto-transport investigations. The sample with rod morphology showed a large extent of phase coexistence compared to the granular sample. Further, with a field-cooling protocol, time-evolution studies were carried out to understand the relaxation of arrested magnetic phases across these morphologically distinct thin films. The results on the devitrification of the arrested magnetic state are interpreted from the point of view of homogeneous and heterogeneous nucleation of the FM phase in the PM matrix with respect to temperature.