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In hybrid improper ferroelectric (Ca,Sr)₃Ti₂O₇, the anharmonic coupling between a stable zone-center polar phonon mode and two unstable zone-boundary non-polar modes, and quasi-2D behavior of c-polarized acoustic modes are theoretically proposed but remain to be experimentally validated. We have performed comprehensive T-dependent single-crystal diffraction, calorimetry, and phonon measurements in (Ca,Sr)₃Ti₂O₇ for x = 0, 0.6, and 0.9, including the behavior across the ferroelectric transition T_c. We also performed first-principles phonon simulations. Our results revealed a strong broadening but little shifting of mean phonon energy on heating across T_c. Among two unstable modes, rotational mode remains robust, but the tilt mode shows substantial softening on heating, consistent with previous studies. However, contrary to previous simulations, our momentum and energy resolved inelastic x-ray scattering measurements did not show a quadratic dispersion of acoustic modes, theoretically associated with a quasi-2D character. Our detailed lattice dynamics study enables to benchmark simulations of anharmonic phonons and associated thermodynamic properties such as thermal expansion and thermal conductivity.