We present a perturbative framework for computing the dynamics of an electronic wave packet launched by an attosecond x-ray pulse in a neutral molecule. The x-ray pulse excites the molecule via both x-ray absorption and impulsive stimulated x-ray Raman scattering (ISXRS), coherently populating both the core-excited states and valence-excited states. We describe the electronic structure within an equation-of-motion coupled-cluster framework, adopting a non-truncated implementation of the sum over states expression characterizing the second-order perturbative description of ISXRS. We study the coherent electronic dynamics in OCS and oxazole utilizing the time-dependent difference electron density, decomposing it in terms of its perturbative components. While the core-excited components dominate the initial stages of the dynamics, the valence-excited components dominate the electronic dynamics on a longer time scale. The pulse polarization controls the symmetry of the states included in the wave packet. We show how the spatial symmetry of the states plays a role in shaping the spatial properties of charge migration. The atomic specificity of the ISXRS process translates directly into the initial localization of the wave packet. This determines the starting point of charge migration, shaping its subsequent evolution.