  Pump-probe response of the spin-orbit coupled Mott insulator Sr$_2$IrO$_4$
reveals a rapid creation of low energy optical weight and suppression of three
dimensional magnetic order on laser pumping. Post pump there is a quick
reduction of the optical weight but a very slow recovery of the magnetic order
- the difference is attributed to weak inter-layer exchange in Sr$_2$IrO$_4$
delaying the recovery of three dimensional magnetic order. We demonstrate that
the effect has a very different and more fundamental origin. Combining
spatio-temporal mean field dynamics and Langevin dynamics on the photoexcited
Mott-Hubbard insulator we show that the timescale difference is not a
dimensional effect but is intrinsic to charge dynamics versus order
reconstruction in a correlated system. In two dimensions itself we obtain a
short, almost pump fluence independent, timescale for charge dynamics while
recovery time of magnetic order involves domain growth and increases rapidly
with fluence. Apart from resolving the iridate Mott problem our approach can be
used to analyse phase competition and spatial ordering in superconductors and
charge ordered systems out of equilibrium.
