Negative thermal expansion (NTE) in tellurium based liquid alloys (GeTe6 and GeTe12) is analyzed through the atomic vibrational properties. Using neutron inelastic scattering, we show that the structural evolution resulting in the NTE is due to a gain of vibrational entropy that cancels out the Peierls distortion. In the NTE temperature range, these competing effects give rise to noticeable changes in the vibrational density of states spectra. Additional first principles molecular dynamics simulations emphasize the role of the temperature dependance of the Ge atomic environment in this mechanism. For comparison, we extended our study to Ge2Sb2Te5 and Ge1Sb2Te4 phase-change materials.