This article investigates the exponential synchronization of fuzzy coupled reaction-diffusion neural networks (RDNNs) under hybrid random cyberattacks. To efficaciously tolerate the cyberattacks and guarantee the expected performance for the proposed systems, a fuzzy-regulation-dependent adaptive spatiotemporal security sampled-data-based event-triggered control scheme (SDBETCS) is first introduced according to distinct fuzzy regulations. In light of the current and latest sampling signals, the threshold parameters can be timely and flexibly updated and the associated adaptive spatiotemporal SDBETCSs can be adaptively regulated for different fuzzy rules. In comparison with the conventional fuzzy SDBETCSs, the designed fuzzy adaptive spatiotemporal SDBETCS can not only reduce the event-triggering frequency but also effectively conserve more finite network communication resources. Through considering a discontinuous Lyapunov functional, a new exponential synchronization criterion is provided for fuzzy coupled RDNNs. Furthermore, a more general fuzzy adaptive spatiotemporal SDBETCS with time-dependent and continuous threshold function is presented to compare with the traditional fuzzy SDBETCS. Finally, demonstrative examples are given to verify the validity and feasibility of the theoretical analysis results and illustrate its potential application in image secure communication.