Amorphous GexSixTe1−2x glasses are studied as a function of composition by a combination of experimental and theoretical methods, allowing for a full description of the network structure in relationship with physico-chemical properties. Calorimetric and thermal measurements reveal that such glasses display an anomalous behavior across a range of compositions xc1=7.5% and <x<xc2=9%, in which is manifested a deep minimum in molar volume, non-reversing enthalpy, and liquid fragility. These anomalies allow defining an intermediate phase, where network rigidity onsets as the content x of Group IV atoms (Ge, Si) are increased. The structural manifestation of these anomalies is understood from 119Sn Mössbauer spectroscopy and First Principles Molecular Dynamics at selected compositions (Ge20Te80, Si20Te80, and Ge10Si10Te80). The numerical models reveal the quite different roles played by the modifier or network cross-linker Ge or Si atoms, Si being more tetrahedral in sp3 geometry, whereas Mössbauer spectroscopy shows that the nature of chemical bonding is dramatically changed around x≃ 8%. The precise evolution of the local structure and chemical bonding ultimately allows understanding the origin of the intermediate phase in these complex tellurides.