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Abstract Self‐organizing memristive nanowire (NW) networks are promising candidates for neuromorphic‐type data processing in a physical reservoir computing framework because of their collective emergent behavior, which enables spatiotemporal signal processing. However, understanding emergent dynamics in multiterminal networks remains challenging. Here experimental spatiotemporal characterization of memristive NW networks dynamics in multiterminal configuration is reported, analyzing the activation and relaxation of network's global and local conductance, as well as the inherent spatial nonlinear transformation capabilities. Emergent effects are analyzed i) during activation, by investigating the spatiotemporal dynamics of the electric field distribution across the network through voltage mapping; ii) during relaxation, by monitoring the evolution of the conductance matrix of the multiterminal system. The multiterminal approach also allowed monitoring the spatial distribution of nonlinear activity, demonstrating the impact of different network areas on the system's information processing capabilities. Nonlinear transformation tasks are experimentally performed by driving the network into different conductive states, demonstrating the importance of selecting proper operating conditions for efficient information processing. This work allows a better understanding of the local nonlinear dynamics in NW networks and their impact on the information processing capabilities, providing new insights for a rational design of self‐organizing neuromorphic systems.