Reentrant glass transition is a new glass-transition phenomenon in which a devitrified liquid reenters a second glassy state and is well-known in some colloidal systems. Reentrant glass transition has been recently discovered in metallic-liquid systems but its ongoing mechanisms remain mostly unknown. Here, the reentrant glass transition of a series of Pd-Ni-P metallic liquids are investigated using fast-calorimetric analyses and ab-initio molecular dynamics simulation. While the amount of heat release of reentrant glass transition in different Pd-Ni-P liquids are similar, the change of liquid kinetics itself results in different reentrant-glass-transition behaviors: the transition kinetics is governed by the fast hopping of P atoms rather than the cooperative liquid motions related with vitrification. The reentrant glass transition is found to be related to medium-range structural ordering process through vertex-sharing of the P-centered polyhedral clusters. The kinetics map of liquid freezing for Pd-Ni-P glass-forming liquids over broad ranges of heating-rate and composition is presented. Display omitted