Although experimentally simulating predator presence helps improve sample sizes in studies of free‐ranging animals, few studies have examined whether auditory playbacks and visual models produce similar results. Additionally, it is unclear if anti‐predator strategies are specific to predator hunting styles in understudied Neotropical pitheciid primates, limiting what we can generalize about this phenomenon across this taxonomic order. We conducted predator simulation experiments to assess whether wild Rylands' bald‐faced saki monkeys (Pithecia rylandsi) recognize predators based solely on acoustic cues, exhibit predator‐specific responses to different predator types, and vary responses to presentations in different sensory modes. In our playback experiments, sakis had weak responses to non‐predator control vocalizations compared to jaguar growls and harpy eagle shrieks. In most predator playbacks, subjects' first glance corresponded to the direction from which simulated predators would typically attack (above vs. below). However, although sakis exhibited appropriate movement responses to harpy playbacks (i.e., descending canopy), they exhibited no clear movement patterns when presented with jaguar playbacks. In contrast, jaguar model experiments consistently elicited fast approaches, mobbing‐style responses, and long alarm calling bouts. Thus, if we had relied on playbacks alone, we might have concluded that sakis have only generalized responses to terrestrial ambush predators. In fact, in all variables measured (e.g., latency, number of calls, and response duration), models of both predator species elicited stronger reactions than playbacks. Results indicate that bald‐faced sakis can identify predators based solely on vocalizations, but do not exhibit predator‐specific escape responses to terrestrial predators based on acoustic cues alone. The differential response to playbacks and models calls into question the reliability of using acoustic‐only stimuli to assess the specificity of anti‐predator behavior to predator hunting styles in some primate species.