A variety of nonequilibrium multi-pulse states can emerge in a mode-locked laser through the interactions between the quasi-continuous-wave background (qCWB) and optical pulses inside the laser cavity. However, they have been long regarded as unpredictable and hardly controllable due to the noise-like nature of the qCWB, and relevant previous studies thus lack a clear understanding of their underlying mechanisms. Here, we demonstrate that the qCWB landscape can be manipulated via optoacoustically mediated interactions between the qCWB and mode-locked pulses, which dramatically alters the behaviors of multi-pulse dynamics in unprecedented manners. In this process, impulsive qCWB modulations are created at well-defined temporal locations, which act as the point emitters and attractive potentials for drifting pulse bunches and soliton rains. Hence, we can transport a single pulse bunch from a certain temporal position to another on the qCWB, and also make the soliton rain created and collided exclusively at specific temporal locations, in sharp contrast to the conventional cases. Our study opens up new possibilities to control the nonequilibrium multi-pulse phenomena precisely in the time domain, which would not only help the observation and clear understanding of undiscovered features of multi-pulse dynamics but offer a practical means of advanced optical information processing.