Cognitive skills undergo protracted developmental changes resulting in proficiencies that are a hallmark of human cognition. One skill that develops over time is the ability to problem solve, which in turn relies on cognitive control and attention abilities. Here we use a novel multimodal neurocognitive network-based approach combining task-related fMRI, resting-state fMRI and diffusion tensor imaging (DTI) to investigate the maturation of control processes underlying problem solving skills in 7-9 year-old children. Our analysis focused on two key neurocognitive networks implicated in a wide range of cognitive tasks including control: the insula-cingulate salience network, anchored in anterior insula (AI), ventrolateral prefrontal cortex and anterior cingulate cortex, and the fronto-parietal central executive network, anchored in dorsolateral prefrontal cortex and posterior parietal cortex (PPC). We found that, by age 9, the AI node of the salience network is a major causal hub initiating control signals during problem solving. Critically, despite stronger AI activation, the strength of causal regulatory influences from AI to the PPC node of the central executive network was significantly weaker and contributed to lower levels of behavioral performance in children compared to adults. These results were validated using two different analytic methods for estimating causal interactions in fMRI data. In parallel, DTI-based tractography revealed weaker AI-PPC structural connectivity in children. Our findings point to a crucial role of AI connectivity, and its causal cross-network influences, in the maturation of dynamic top-down control signals underlying cognitive development. Overall, our study demonstrates how a unified neurocognitive network model when combined with multimodal imaging enhances our ability to generalize beyond individual task-activated foci and provides a common framework for elucidating key features of brain and cognitive development. The quantitative approach developed is likely to be useful in investigating neurodevelopmental disorders, in which control processes are impaired, such as autism and ADHD.