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Earthquakes are complex physical processes driven by stick-slip motion on a sliding fault. After the main event, a series of aftershocks is usually observed. The latter are loosely defined as earthquakes that follow a parent event and occur within a prescribed space-time window. In seismology, it is currently not possible to establish an unambiguous causal relation between events, and the nearest-neighbor metric is commonly used to distinguish aftershocks from independent events. Here, we employ a soft-glass model as a proxy for earthquake dynamics, previously shown to be able to correctly reproduce the phenomenology of earthquakes, together with a technique that allows us to clearly separate independent and triggered events. We show that aftershocks in our plastic event catalog follow Omori's law with slopes depending on the triggering mode, an observation possibly useful for seismology. Finally, we confirm that the nearest-neighbor metric is indeed effective in separating independent events from aftershocks.