Temporal interfaces enable dynamic wave control but face a fundamental bottleneck: temporal reflection and refraction amplitudes depend on incident momentum because the projection coefficients between pre and postquench eigenstates—defined by biorthogonal overlaps in the non-Hermitian case—are generically momentum dependent, which distorts broadband wave packets. We develop a projection-operator framework for temporal scattering and show that when a $\mathcal{PT}$-symmetry phase transition occurs across the interface, the final eigenbasis satisfies a phase-transition-induced orthogonality condition, which renders the overlap magnitudes momentum independent and thus yields broadband-stable temporal splitting. Experiments in an electrically reconfigurable acoustic-cavity lattice confirm momentum-robust scattering over a finite bandwidth, and our analysis further reveals nonorthogonality-induced amplification/attenuation and a null-excitation criterion for stable temporal boundary states. These results position geometric projection as a unifying mechanism for non-Hermitian temporal physics and a practical route to versatile time-domain devices.

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• Acoustic metamaterials
• Non-Hermitian systems
• Tight-binding model