It depends on their delay and the scintillator time resolution.
Sorry, I presently miss a suitable reference at hand.
In the simulation, in addition to the global TIME-CUT you initially mentioned, one could try to filter the DETECT spectrum as a function of the aforementioned delay between subsequent energy deposition contributions. To this purpose, you may want to take a look at the use of the comscw routine as discussed in this contemporary DETECT thread. In your case, the relevant filter variable (for possible multiple DETECT cards of tailored names) would not be the particle species, rather its age (ATRACK in trackr.inc).