In this paper, the spectral evolution properties and gain dynamics in hybrid rare-earth-Raman fiber amplifiers (H-RFAs) are demonstrated theoretically. Spectral broadening mechanisms and design strategies are given for H-RFAs based on two different types of pump schemes for generating the pump laser of Raman gain. As for the diode-pumped scheme, only a temporal stable pump laser of Raman gain is required to achieve the narrow-linewidth operation of an ultimate Raman fiber laser. As for the tandem-pumped scheme, both temporal stable pump lasers of rare-earth gain and Raman gain are required to achieve narrow-linewidth operation. The physical mechanism behind the phenomenon is the diversity of the pump-to-signal noise transfer property when applying different pump sources of rare-earth gain.