<p>Pump-probe spectroscopy is a powerful technique for investigating ultrafast exciton dynamics. However, developing a theoretical framework for modeling the transient response in photoexcited materials has remained a challenge. Here, we present a first-principles approach based on a non-equilibrium extension to the Bethe-Salpeter equation to simulate pump-probe spectroscopy and disentangle electronic and thermal contributions to the transient response. Applied to three prototypical semiconductors, i.e., the transition-metal dichalcogenide WSe₂, the metal halide perovskite CsPbBr₃, and the transition-metal oxide TiO₂, the method obtains the transient spectra in excellent agreement with experiment. Our analysis reveals that distinct renormalization mechanisms shape the spectral shifts: Photoinduced Coulomb screening, as the dominant electronic effect, drives excitonic blueshifts, while Pauli blocking plays a minor role. Thermal effects induce redshifts on the picosecond time scale. We further demonstrate how key parameters, such as carrier population distribution, pump wavelength, and pump polarization, impact the transient absorption spectra, which offer direct control over the exciton resonance energy. Our approach establishes a framework for interpreting and tailoring pump-probe spectra, providing guidelines for exciton engineering and thus contributing to the design of energy-selective optoelectronic devices.</p>