Mode-locked fiber lasers are an ideal platform for an ultrafast nonlinear physics study, and they have shown many intriguing, yet not fully understood, phenomena such as the optical rogue waves (ORWs) and noise-like pulses (NLPs). However, one of the major obstacles in the study of fiber laser dynamics is the lack of practical measurement techniques for round-trip tracking, and single-shot, real-time observation in the time domain at sub-picosecond (ps) resolution. Here we demonstrate an automatically synchronized characterization of NLPs using a parametric time magnifier. The round-trip evolution of ultrafast temporal structures in the noise-like pulses has been experimentally resolved at sub-ps resolution, to the best of our knowledge, for the first time, and ORWs have been identified.