Compared to CTMQC, the SH framework brings several advantages, e.g., better numerical stability, reliable description of nuclear WP branching in the asymptotic regions and energy conservation. However, the inconsistency problem between wave function and active states in SH might still exist in CTSH, which could lead to incorrect decoherence in the XF part and incorrect trajectory hopping in the SH part. In this paper, we investigate this inconsistency problem in CTSH and propose a consistent decoherence scheme for SH-based coupled-trajectory dynamics. Along with a novel nuclear density reconstruction approach, our new sign-consistent CTSH (SC-CTSH) method can obtain accurate quantum momentum, and thus impose correct decoherence.