  Emergent symmetry is one of the characteristic phenomena in deconfined
quantum critical point (DQCP). As its nonequilibrium generalization, the dual
dynamic scaling was recently discovered in the nonequilibrium imaginary-time
relaxation dynamics in the DQCP of the $J$-$Q_3$ model. In this work, we study
the nonequilibrium imaginary-time relaxation dynamics in the $J$-$Q_2$ model,
which also hosts a DQCP belonging to the same equilibrium universality class.
We not only verify the universality of the dual dynamic scaling at the critical
point, but also investigate the breakdown and the vestige of the dual dynamic
scaling when the tuning parameter is away from the critical point. We also
discuss its possible experimental realizations in devices of quantum computers.
