Strong dipole-exchange interactions due to spontaneously produced contaminant states can trigger rapid dephasing in many-body Rydberg ensembles [E. A. Goldschmidt et al., Phys. Rev. Lett. 116, 113001 (2016)]. Such broadening has serious implications for many proposals to coherently use Rydberg interactions, particularly Rydberg dressing proposals. The dephasing arises as a runaway process where the production of the first contaminant atoms facilitates the creation of more contaminant atoms. Here we study the time dependence of this process with stroboscopic approaches. Using a pump-probe technique, we create an excess "pump" Rydberg population and probe its effect with a different "probe" Rydberg transition. We observe a reduced resonant pumping rate and an enhancement of the excitation on both sides of the transition as atoms are added to the pump state. We also observe a time scale for population growth that is significantly shorter than predicted by homogeneous mean-held models, as expected from a clustered growth mechanism where high-order correlations dominate the dynamics. These results support earlier works and confirm that the time scale for the onset of dephasing is reduced by a factor which scales as the inverse of the atom number. In addition, we discuss several approaches to minimize these effects of spontaneous broadening, including stroboscopic techniques and operating at cryogenic temperatures. It is challenging to avoid the unwanted broadening effects, but under some conditions they can be mitigated.