The dynamics of the interconnected electron–nuclear spin system affect the response bandwidth of atomic-spin inertial measurement and its ability to reject external magnetic-field interference and are important for performance evaluation and operating-parameter selection. An axial steady-state operating point is obtained from the full six-dimensional nonlinear Bloch model under spin-exchange relaxation-free (SERF) conditions. A local transverse model in complex variables is derived and checked against the numerical Jacobian and small-perturbation time-domain responses. With the operating point, diagonal dynamics, and input vectors fixed, off-diagonal coupling terms are set to zero or continuously scaled to compare changes in the transverse poles and the inertial and magnetic-field responses. At a rotation-step amplitude of 0.0125 rad/s, the normalized root-mean-square error between the outputs of the two models is 0.00686%. In the reference case with bidirectional coupling, the transverse slow-pole decay rate increases from 0.25 s?1 to 37.91 s?1. The contribution of slow nuclear-spin dynamics to the electron-spin output extends the settling time from 0.0191 s to 0.1541 s. When both off-diagonal coupling coefficients are increased by 30%, the inertial response bandwidth increases from 4.18 Hz to 8.34 Hz. Modal decomposition shows that the fast- and slow-mode contributions to the magnetic-field dc gain nearly cancel in the reference case, while their different time evolutions can still produce a transient peak. The magnitude and complex phase of the coupling product jointly affect the transverse poles, whereas the measurement response also depends on modal input excitation and output projection. These results apply to small perturbations near the specified operating point and the local coupling-term variations examined. The findings provide a theoretical reference for system parameter design that considers both inertial response bandwidth and magnetic-field rejection.