Manipulating electron spins on ultrashort timescales shows promise in the field of data processing. Because of the direct electron-photon coupling, photons have been widely used for such studies, but not phonons. Here we tie coherent phonon detection to transient spin populations. We optically excite gigahertz picosecond phonon wave packets in a metal-coated GaAs slab containing GaAs/Al0.4Ga0.6As multiple quantum wells on the opposite side. Before the phonon wave-packet arrival, circularly polarized light induces a transient spin polarization. Phonon-induced ultrafast polarization rotation and reflectivity changes contingent on the transient spin population are detected by a heterodyne modulation technique. With an analytical model, we posit the presence of significant second-order interactions, enabled by spins, in the coherent-phonon optical detection. Applications include transient spin population monitoring and novel spintronic nanodevices.