This paper focuses on the distributionally robust dispatch for integrated transmission-distribution (ITD) systems via distributed optimization. Existing distributed algorithms usually require synchronization of all subproblems, which could be hard to scale, resulting in the under-utilization of computation resources due to the subsystem heterogeneity in ITD systems. Moreover, the most commonly used distributionally robust individual chance-constrained dispatch models cannot systematically and robustly ensure simultaneous security constraint satisfaction. To address these limitations, this paper presents a novel distributionally robust joint chance-constrained (DRJCC) dispatch model for ITD systems via asynchronous decentralized optimization. Using the Wasserstein-metric based ambiguity set, we propose data-driven DRJCC models for transmission and distribution systems, respectively. Furthermore, a combined Bonferroni and conditional value-at-risk approximation for the joint chance constraints is adopted to transform the DRJCC model into a tractable conic formulation. Meanwhile, considering the different grid scales and complexity of subsystems, a tailored asynchronous alternating direction method of multipliers (ADMM) algorithm that better adapts to the star topological ITD systems is proposed. This asynchronous scheme only requires local communications and allows each subsystem operator to perform local updates with information from a subset of, but not all, neighbors. Numerical results illustrate the effectiveness and scalability of the proposed model.