  We investigate the anomalous photo-induced band renormalization in correlated
materials, exemplified by the case of Ta$_2$NiSe$_5$. The manifestation of this
anomaly is characterized by the alternating direction of band shift in response
to changes in the laser parameters or electron momentum. We attribute the
phenomena to the band inversion of the material and the selective excitation of
a high-lying flat band, leading to the competition between the Hartree shift
and the order collapse. These findings are based on {\it ab initio} determined
effective model for Ta$_2$NiSe$_5$, in which we incorporate high-lying states
and the time-dependent GW simulation to follow the non-equilibrium dynamics
induced by the laser. Our findings reveal the sensitivity of the
non-equilibrium electronic dynamics to the band structure and laser protocols,
providing valuable guidance for the selection of suitable materials and lasers
in the engineering of band structures.
