We explore the predictive power of cosmological, hydrodynamical simulations for stellar phase space substructure and velocity correlations with the Auriga simulations and Aurigaia mock-Gaia catalogues. We show that at the solar circle the Auriga simulations commonly host phase space structures in the stellar component that have constant orbital energies and arise from accreted subhaloes. These structures can persist for a few Gyrs, even after coherent streams in position space have been erased. We also explore velocity two-point correlation functions and find this diagnostic is not deterministic for particular clustering patterns in phase space. Finally, we explore these structure diagnostics with the Aurigaia catalogues and show that the current catalogues have the ability to recover some structures in phase space but careful consideration is required to separate physical structures from numerical structures arising from catalogue generation methods.