Decision-making is an essential cognitive process by which we interact with the external world. However, attempts to understand the neural mechanisms of decision-making are limited by the current available animal models and the technologies that can be applied to them. Here, we build on the renewed interest in using tree shrews (Tupaia Belangeri) in vision research and provide strong support for them as a model for studying visual perceptual decision-making. Tree shrews learned very quickly to perform a two-alternative forced choice contrast discrimination task, and they exhibited differences in response time distributions depending on the reward and punishment structure of the task. Specifically, they made occasional fast guesses when incorrect responses are punished by a constant increase in the interval between trials. This behavior was suppressed when faster incorrect responses were discouraged by longer inter-trial intervals. By fitting the behavioral data with two variants of racing diffusion decision models, we found that the between-trial delay affected decision-making by modulating the drift rate of a time accumulator. Our results thus provide support for the existence of an internal process that is independent of the evidence accumulation in decision-making and lay a foundation for future mechanistic studies of perceptual decision-making using tree shrews.