We propose to clarify the topology of quasi-Hermitian Chern insulators by quantum quench dynamics. The Bloch Hamiltonian of a pseudo-Hermitian Chern insulator is defined based on the q-modified Pauli matrices associated with the modified algebraic representation. We demonstrate the bulk-surface duality of the quasi-Hermitian phase and further build concrete relationships between static band topology and quench dynamics with respect to the time-averaged spin texture. The results also generalize to the completely non-equilibrium case, where the post-quenching evolution is governed by the Floquet-quasi-Hermitian Hamiltonian. Furthermore, we achieve a seemingly challenging model in double-layer lattices and propose a possible scheme for detecting dynamics in double-quenching protocols.
