Liveness is a well-known problem with Digital Musical Instruments (DMIs). When used in performances, DMIs provide less visual information than acoustic instruments, preventing the audience from understanding how the musicians influence the music. In this paper, we look at this issue through the lens of causality. More specifically, we investigate the attribution of causality by an external observer to a performer, relying on the theory of apparent mental causation. We suggest that the perceived causality between a performer's gestures and the musical result is central to liveness. We present a framework for assessing attributed causality and agency to a performer, based on a psychological theory which suggests three criteria for inferred causality. These criteria then provide the basis of an experimental study investigating the effect of visual augmentations on audience's inferred causality. The results provide insights on how the visual component of performances with DMIs impacts the audience's causal inferences about the performer. In particular we show that visual augmentations help highlight the influence of the musician when parts of the music are automated, and help clarify complex mappings between gestures and sounds. Finally we discuss the potential wider implications for assessing liveness in the design of new musical interfaces.