Our behavior entails a flexible and context-sensitive interplay between brain areas to integrate information according to goal-directed requirements. However, the neural mechanisms governing the entrainment of functionally specialized brain areas remain poorly understood. In particular, the question arises whether observed changes in the regional activity for different cognitive conditions are explained by modifications of the inputs to the brain or its connectivity? We observe that transitions of fMRI activity between areas convey information about the tasks performed by 19 subjects, watching a movie versus a black screen (rest). We use a model-based framework that explains this spatiotemporal functional connectivity pattern by the local variability for 66 cortical regions and the network effective connectivity between them. We find that, among the estimated model parameters, movie viewing affects to a larger extent the local activity, which we interpret as extrinsic changes related to the increased stimulus load. However, detailed changes in the effective connectivity preserve a balance in the propagating activity and select specific pathways such that high-level brain regions integrate visual and auditory information, in particular boosting the communication between the two brain hemispheres. These findings speak to a dynamic coordination underlying the functional integration in the brain.