It has been suggested that radial transport in turbulent plasmas may be nonlocal and non-Markovian. In this paper the transport of test particles in the global, electromagnetic, three-dimensional code CUTIE [A. Thyagaraja and et al. , Phys. Plasmas 12 , 090907 (2005)] is characterized. This code includes a nonlinear feedback mechanism between the meso- and macroscales that are expected to lead to some degree of self-organization that should be reflected in the trajectories of the tracer particles. Several techniques are used to analyze these trajectories, and indeed long-range spatial and temporal correlations are detected, indicating that effective global radial transport in CUTIE does not satisfy the traditional paradigm of diffusive transport. Part of this result can be explained from the existence of propagating ballistic events, and another part from a dependence of local transport properties on the safety factor: local transport is found to depend sensitively on the position relative to specific rational surfaces.