A two-step phase separation was imposed to a binary mixture of deuterated polybutadiene and protonated polyisoprene with nearly critical composition in the following way: the system was first subjected to phase separation via spinodal decomposition (SD) so that the system developed coexisting two phases characteristics of the late stage of SD (the first-step phase separation). It was then brought into a deeper quench so that both two phases again fell into spinodal region and hence further SD took place within each phase (the second-step phase separation at T-2). In the very early stage after this second-step phase separation, the two-phase structure developed in the first-step phase separation was almost unchanged with time, but the composition fluctuation was newly developed within each phase, giving rise to an excess light scattering (LS) at large scattering vectors. The very early stage in this second-step phase separation process was studied by time-resolved LS. We found that the early-stage SD after the second-step phase separation at T-2 can be well described by the linearized theory of SD. However the characteristic parameters, especially the collective diffusivity, obtained from the linear analysis, were different from those obtained by the single-step SD at T-2 for the corresponding single-phase mixtures. The results unveil an intriguing effect of initial structure or space confinement on early stage SD, reflecting an intrinsically nonlinear phenomenon.