The evolution of a V-type three-level system is studied, whose two resonances are coherently excited and coupled by two ultrashort laser pump and probe pulses, separated by a varying time delay. We relate the quantum dynamics of the excited multilevel system to the absorption spectrum of the transmitted probe pulse. In particular, by analyzing the quantum evolution of the system, we interpret how atomic phases are differently encoded in the time-delay-dependent spectral absorption profiles when the pump pulse either precedes or follows the probe pulse. This scheme is experimentally applied to atomic Rb, whose fine-structure-split 5s (2)S{1/2}→5p(2)P{1/2} and 5s(2)S_{1/2}→5p(2)P{3/2} transitions are driven by the combined action of a pump pulse of variable intensity and a delayed probe pulse. The provided understanding of the relationship between quantum phases and absorption spectra represents an important step towards full time-dependent phase reconstruction (quantum holography) of bound-state wave packets in strong-field light-matter interactions with atoms, molecules, and solids.