  We investigate slow non-equilibrium dynamical processes in two-dimensional
$q$--state Potts model with both ferromagnetic and $\pm J$ couplings. Dynamical
properties are characterized by means of the mean-flipping time distribution.
This quantity is known for clearly unveiling dynamical heterogeneities. Using a
two-times protocol we characterize the different time scales observed and
relate them to growth processes occurring in the system. In particular we
target the possible relation between the different time scales and the spatial
heterogeneities originated in the ground state topology, which are associated
to the presence of a backbone structure. We perform numerical simulations using
an approach based on graphics processing units (GPUs) which permits to reach
large system sizes. We present evidence supporting both the idea of a growing
process in the preasymptotic regime of the glassy phases and the existence of a
backbone structure behind this processes.
