<p>Raman random fiber laser (RRFL) possesses rich physical properties of spectral, temporal, and spatial domains due to its unique feedback mechanism and complex nonlinear effects. Characterizing and controlling the microscopic evolution dynamics of RRFL are crucial to driving breakthrough advances in fields such as inertial confinement fusion and fundamental physics. In this work, a novel experimental and theoretical analysis of the evolution of the temporal spectral correlations of the RRFL in the transition and steady states is conducted. In the transitional state, the microscopic dynamics of the RRFL excitation process is revealed comprehensively: the temporal-correlation growth curve contrasts with that of resonant-cavity lasers, and the formation and degradation of spectral correlation are observed. In the steady state, the overall spectrum is characterized by partial correlation, and the correlation characteristics of RRFL mainly originate from the spectral random spikes, which offers a novel dimension for the precise control of RRFL correlation. This work provides new insights into underlying physical properties of continuous broadband lasers, offering key guidance for laser design, control, and applications.</p>