We describe the precise mechanism behind the rapid and large spectral broadening in the early stages of supercontinuum generation in submicron-core glass waveguides. The first spectral and temporal breathing period of higher-order solitons activates the solitonic resonant radiation by means of energy bursts. We demonstrate that this "activation length" is largely independent of the Raman effect but can be efficiently controlled by changing the input pulse chirp. Energy transfer between the input pulse and its resonant radiations has a marked steplike character, and can reach a large efficiency. This will lead to the design of devices based on millimeter-size fibers, which are able to emit a clean, coherent, and controllable spectrum.