First-principles, real-time-cumulant, and Bethe-Salpeter-equation calculations fully capture the detailed satellite structure that occurs in response to the sudden creation of the core hole in both photoemission and x-ray absorption spectra of the transition-metal compounds SrTiO3 and rutile TiO2. Analysis of the excited-state, real-space charge-density fluctuations betrays the physical nature of these many electron excitations that are shown to reflect the materials' solid-state electronic structure and chemical bonding. This first-principles development of the cumulant-based core hole spectral function is generally applicable to other systems and should become a standard tool for all similar spectroscopic analysis going beyond the quasiparticle physics of the photoelectric effect.