With multi-stereoscopy technology, novel projection-based immersive systems now can support multiple users by providing each one with an independent stereoscopic view of the virtual scene. When users work face-to-face, they may have an incorrect view if objects are located between them. In this case, avatars can be introduced to enable face-to-face interaction in the virtual world, whereas they are side-by-side in the real device. As a consequence, such multi-user systems provide the users with a new kind of perceptual immersion and related cognitive experiences, because users must handle both information from the real world (i.e., other users' bodies) and those from the virtual scene (i.e., other users' avatars) at the same time. In this study, we experimentally created special interaction situations to examine the perceptual conflicts generated by the dual-presence of the real and virtual visual and audio stimuli. In a two-user scenario, participants performed an object-picking task according to three types of instructions (verbal, gestural, or multimodal instructions) given by an experimenter. This co-located experimenter was also virtually present by an avatar in the virtual world to enable face-to-face interactions with the participants. Our goal was to observe to what extent the perceptual conflicts induced by the dual-presence of the experimenter can be integrated without significantly altering the performance of the participants. For that, we studied the influence of such perceptual conflicts on participants' choice of collaborator (whether they interacted with the avatar or the real experimenter) and on their task efficiency. As the results showed, first users had an a priori choice of collaborator (avatar or real person) and this choice did not change under different experimental conditions. Second, perceptual conflicts had an impact on users' performance in terms of task completion time. We discuss the implications of these results for designing a better immersive system for co-located collaboration between multiple users.