A seamless numerical model of coupled multiphase flow and inertial mechanics in fractured porous media is proposed. The model develops an automatic time step size control method to efficiently and accurately capture transitions between flow with small deformation, quasi-static slip, and dynamic rupture with seismic wave propagation. The model utilizes a mixed and embedded approach that represents fractures explicitly. The mixed discretization combines an extended finite element method (XFEM) with a projection embedded discrete fracture and matrix (pEDFM) finite volume method. Mechanical inertia is approximated implicitly using a stable Newmark scheme, and fracture contact constraints for stick-slip conditions are enforced by a Lagrange Multiplier approach that is stabilized by Polynomial Pressure Projection (PPP). The temporal adaption method combines discretization error, Coulomb friction, and slip rate considerations to capture pre-seismic triggering, co-seismic spontaneous rupture, and arrest. The model is applied to simulate multiple cycles of induced seismic rupture under various multiphase fluid production and injection scenarios. This is enabled by time step size control to automatically span transitions across seven orders of magnitude in timescales.