The continuous and isothermal crystallization diagrams of the Pt42.5Cu27Ni9.5P21 and the Pt60Cu16Co2P22 bulk glass forming compositions are determined using calorimetric experiments. In the case of the Pt42.5Cu27Ni9.5P21 bulk metallic glass, the formation of the primary crystalline phase can be prevented by rapid cooling in a conventional DSC. In contrast, for similar cooling conditions, the formation of the primary precipitating compound in Pt60Cu16Co2P22 cannot be prevented in a conventional DSC as also observed in in-situ synchrotron X-ray scattering experiments. This is attributed to a critical overheating, above which remaining structures dissolve, resulting in a drastic increase of the degree of undercooling, similar to what is observed in Zr-based BMGs. Using the classical nucleation theory, the combined thermodynamic and kinetic data are used to model the isothermal crystallization data for Pt42.5Cu27Ni9.5P21, yielding an interfacial energy value of 0.11 J/m2 between the primary nucleating crystal and the liquid. This value is three times higher than the value for good Zr-based glass-formers, suggesting that the interfacial energy plays a pivotal role in the exceptionally high glass-forming ability of Pt-P-based systems and compensates for the fragile liquid behavior and the large driving force for crystallization.