Musical interaction is a unique model for understanding humans' ability to align goals, intentions, and actions, which also allows for the manipulation of participants' internal predictive models of upcoming events. Here we used polyrhythms to construct two joint finger tapping tasks that even when rhythmically dissimilar resulted in equal inter-tap intervals (ITIs). Thus, behaviourally a dyad of two musicians tap isochronously at the same rate, yet with their own distinct rhythmical context model (RCM). We recruited 22 highly skilled musicians (in 11 dyads) and contrasted the effect of having a shared versus non-shared RCM on dyads' synchronization behaviour. As expected, tapping synchronization was significantly worse at the start of trials with non-shared models compared to trials with a shared model. However, the musicians were able to quickly recover when holding dissimilar predictive models. We characterised the directionality in the tapping behaviour of the dyads and found patterns mostly of mutual adaptation. Yet, in a subset of dyads primarily consisting of drummers, we found significantly different synchronization patterns, suggesting that instrument expertise can significantly affect synchronization strategies. Overall, this demonstrates that holding different predictive models impacts synchronization in musicians performing joint finger tapping.