Cognition arises through the interaction of distributed, but connected, brain regions. Each region can exhibit neuronal dynamics ranging from asynchronous spiking to richly patterned spatio-temporal activity, where coordinated trial-to-trial fluctuations within the population can be described by a small number of shared latent variables. Even though recent technological advances have allowed simultaneous recordings from multiple brain areas, it is still unknown how diverse and complex within-area neuronal dynamics affect between-area interactions. Using a spiking network model exhibiting a wide range of neuronal dynamics, we show that communication efficacy, as assessed by linear measures, depends on the origin of low-dimensional shared variability. More specifically, a mismatch in within-area dimensionality or a misalignment of shared variability between upstream and downstream areas compromise communication. However, even in scenarios with seemingly weak linear communication, the downstream area is effectively driven by the upstream activity. These results expose the limitations of linear measures when analyzing between-area communication in circuits with diverse neuronal dynamics.