We revisit quantum $\varphi$-synchronization in a dissipatively coupled cavity-magnon system and formulate the calculation within one consistent system-bath model. A Hermitian photon-magnon interaction of strength $g$ is supplemented by a common Markov channel $L_c=\sqrt{2\mathrm{\Gamma }}(a-im)$. Interference between coherent and dissipative coupling produces the asymmetric rates ${\lambda }_1=g-\mathrm{\Gamma }$ and ${\lambda }_2=g+\mathrm{\Gamma }$, while the same channel necessarily supplies correlated input noise. We derive the quantum Langevin equations from the input-output model and show explicitly that the reduced adjoint Lindblad map is not an operator-algebra homomorphism; canonical commutators are instead preserved by the full Langevin dynamics, including the input fields. For the linear Gaussian system, a quantum Itô product calculation gives the closed second-moment equation $\dot{V}=AV+V{A}^{\mathsf{T}}+D$, with a nondiagonal diffusion matrix fixed by the common bath. This construction answers how the higher-order moments are obtained without raising a first-moment solution to a power. At resonance the drift spectrum has an exceptional point at ${\mathrm{\Gamma }}_{\mathrm{EP}}=\sqrt{g^2-{(\kappa -\gamma )}^2/4}$. For $g/\kappa =2$, $\gamma /\kappa =0.1$, a vacuum common bath, and a magnon-bath occupation $n_m=10$, the fluctuation measure $S_q^{\varphi }$ increases from 0.256 at $\mathrm{\Gamma }=0$ to 0.672 at the exceptional point; the full measure, which also retains the mean-amplitude mismatch, increases from 0.243 to 0.632. A thermal-bath control shows that this improvement is caused by reservoir engineering rather than by spectral coalescence alone. The exceptional point is therefore an experimentally identifiable spectral marker of the strong-dissipation regime, not an independent source of noiseless topological enhancement.

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• Quantum optics
• Synchronization