SARS-CoV-2 spreads by infectious aerosols and droplets from the respiratory tract. Masks and respirators can reduce the transmission of infectious respiratory diseases by collecting these aerosols at the source. The ability of source control devices to block aerosols can be tested by expelling an aerosol through a headform using constant airflows, which are simpler, or cyclic airflows, which are more realistic but require more complex methods. Experiments with respirators found that using cyclic vs. constant flows affected the amount of aerosol inhaled, but similar comparisons have not been made for source control devices with exhaled aerosols. We measured the collection efficiencies for exhaled aerosols for two cloth masks, two medical masks with and without an elastic mask brace, a neck gaiter, and an N95 filtering facepiece respirator using 15 L/min and 85 L/min constant and cyclic flows and a headform with pliable skin. The collection efficiencies for the 15 L/min cyclic flow, 15 L/min constant flow, and 85 L/min constant flow were not significantly different in most cases. The apparent collection efficiencies for the 85 L/min cyclic flow were artificially increased by rebreathing and refiltration of the aerosol from the collection chamber. The collection efficiencies correlated well with the fit factors (ρ > 0.95) but not the filtration efficiencies (ρ < 0.54). Our results suggest that the aerosol collection efficiency measurements of source control devices are comparable when testing the devices using either constant or cyclic airflows and that the potential for aerosol rebreathing must be considered when conducting experiments.