We address the stability of a tunable hybrid laser based on a III-V Reflective Semiconductor Optical Amplifier (RSOA) edge-coupled with a Silicon Photonic (SiPh) dispersive mirror through a model of time-delayed algebraic differential equations that accounts for the narrow band mirror. Our results allow to (i) analyze the stability of single mode lasing, (ii) quantify the impact of the mirror bandwidth on the damping of the laser relaxation oscillations and the emergence of photon-photon resonance, and (iii) study the tolerance of the laser to the external optical feedback. Thanks to this analysis, we find a mirror design that gives ultra-high stability up to an external feedback level of -10 dB. The aim of the work is providing a tool for understanding and interpreting the dynamics of these lasers and design configurations for isolator-free operation.