We numerically study the impacts of introducing a minute continuous-wave (CW) trigger on the properties of picosecond supercontinuum (SC) generation. We show that this simple triggering approach enables active control of not only the bandwidth, but more importantly the temporal coherence of SC. Detailed numerical simulations suggest that depending on the wavelength of the CW-trigger the multiple higher-order four-wave mixing (FWM) components generated by the CW-trigger can create either a relatively more stochastic or a more deterministic beating effect on the pump pulse, which has significant implications on how soliton fission and the onset of SC are initiated in the presence of noise. By controlling the CW-trigger wavelengths, the rogue solitons emerged in SC generation can exhibit high-degree of temporal coherence and pulse-to-pulse intensity stability. The present study provides a valuable insight on how the initial soliton fission can be initiated in a more controllable manner such that SC generation with both high temporal coherence and stability can be realized.