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We revisit the quantitative analysis of the ultrafast magneto-acoustic experiment in a freestanding nickel thin film by Kim and Bigot [1] by applying our recently proposed approach of magnetic and acoustic eigenmodes decomposition by Vernik et al. [2]. We show that the application of our modeling to the analysis of time-resolved reflectivity measurements allows for the determination of amplitudes and lifetimes of standing perpendicular acoustic phonon resonances with unprecedented accuracy. The acoustic damping is found to scale as $\proptoω^2$ for frequencies up to 80~GHz and the peak amplitudes reach $10^{-3}$. The experimentally measured magnetization dynamics for different orientations of an external magnetic field agrees well with numerical solutions of magneto-elastically driven magnon harmonic oscillators. Symmetry-based selection rules for magnon-phonon interactions predicted by our modeling approach allow for the unambiguous discrimination between spatially uniform and non-uniform modes, as confirmed by comparing the resonantly enhanced magneto-elastic dynamics simultaneously measured on opposite sides of the film. Moreover, the separation of time scales for (early) rising and (late) decreasing precession amplitudes provide access to magnetic (Gilbert) and acoustic damping parameters in a single measurement.