Blasting excavation generates transient P-waves that significantly impact tunnel stability. For water-filled diversion tunnels, the dynamic response of the surrounding rock differs from conventional dry tunnels. Most existing analytical studies focus on the steady-state solution and single-lined tunnels, rarely accounting for composite linings or the presence of water. This paper investigates the transient stability response of deep-buried circular composite lining diversion tunnels under transient P-wave disturbances. The fluid within the tunnel is treated as a distinct medium, and the tunnel-lining interface is considered a non-ideal contact surface. By applying Fourier synthesis, wave function expansion, and trapezoidal quadrature formula, an analytical solution is derived. Validation through comparison with existing literature demonstrates the method's effectiveness. The study analyzes the effects of Poisson's ratio of surrounding rock, the non-ideal interface's elastic coefficient, and the disturbance's loading duration on the dynamic stress concentration coefficient. Results indicate that the compressive stress concentrations occur at the roof and floor, while tensile counterpart concentrations appear at the two sidewalls during dynamic disturbance. As Poisson's ratio increases, there is a transition from tensile to compressive stress concentration, with a gradual degree in compressive stress intensity. Poor contact between the rock mass and liner induces oscillations in the stress time-history curve. The dynamic response converges accordingly as the elastic coefficients of an imperfect interface approach those of a perfect interface. With increasing blasting load duration, peak dynamic stress around the roof and floor initially rises, then stabilizes, while stress at the sidewalls initially decreases before leveling off.