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The quantum paraelectric behavior and strongly anharmonic lattice dynamics of SrTiO₃ have attracted interest for decades. Inelastic neutron scattering (INS) measurements of SrTiO₃ reveal an anomalous evolution of transverse acoustic (TA) phonon intensity with temperature as the transverse optic (TO) mode softens. This reflects the incipient ferroelectric (FE) instability near the quantum critical point and couplings between TA and TO phonons. The experimental trends are confirmed and rationalized using DFT simulations including anharmonic renormalization. By analyzing the temperature-dependent force constants (FC) and eigenvectors, it is found that the structure factors of phonon modes change dramatically with temperature, as a direct consequence of the anharmonicity in this system. We identify that changing Ti and O eigenvectors, originating from FC changes in the Ti-O bonds, are responsible for these striking observations. These results establish how temperature-dependent phonon intensities from INS can provide direct insights into the behavior of phonon eigenvectors, and show how first-principles simulations can rationalize such anharmonic effects.