Sensorimotor synchronisation (SMS) is prevalent and readily studied in musical settings, as most people are able to perceive and synchronise with a beat (e.g., by finger tapping). We took an individual differences approach to understanding SMS to real music characterised by expressive timing (i.e., fluctuating beat regularity). Given the dynamic nature of SMS, we hypothesised that individual differences in working memory and auditory imagery—both fluid cognitive processes—would predict SMS at two levels: (1) mean absolute asynchrony (a measure of synchronisation error) and (2) anticipatory timing (i.e., predicting, rather than reacting to beat intervals). In Experiment 1, participants completed two working memory tasks, four auditory imagery tasks, and an SMS-tapping task. Hierarchical regression models were used to predict SMS performance, with results showing dissociations among imagery types in relation to mean absolute asynchrony, and evidence of a role for working memory in anticipatory timing. In Experiment 2, a new sample of participants completed an expressive timing perception task to examine the role of imagery in perception without action. Results suggest that imagery vividness is important for perceiving and control is important for synchronising with irregular but ecologically valid musical time series. Working memory is implicated in synchronising by anticipating events in the series.