Spacecrafts observe signatures of duskside magnetic reconnection in the Earth's magnetotail associated with the presence of oxygen (O+) ions of ionospheric origin. The exact role of O+ ions in mediating reconnection remains largely unknown due to the local nature of observational techniques. We analyze results from global three-dimensional hybrid (kinetic ions, fluid electrons) simulations of O+ outflows and demonstrate that oxygen ions, escaping from the top of the ionosphere into the lobes, may cause disruptions on the duskside of the proton-formed magnetotail, adding up to its turbulent, unsteady nature. These O+ ions are shown to be capable of inducing magnetic flux ropes in the current sheet that thins out toward the dusk flank of the magnetotail due to Hall and ion kinetic effects. Unlike magnetohydrodynamics (MHD) simulations, where dawn-dusk magnetotail asymmetries may develop due to nonuniform ionospheric conductivity, the hybrid simulations demonstrate duskside tail disruptions on much faster ion gyroscales. Plain Language Summary Being one of the most important and ubiquitous elements of space weather, magnetic reconnection (breaking and merging of oppositely directed magnetic field lines in a plasma) globally governs the dynamics of the Sun-Earth system. Current approaches to investigating this phenomenon in the Earth's magnetotail (the extension of the magnetosphere in the antisunward direction) largely assume that the magnetosphere is dominated by solar wind plasma, which mostly consists of protons. Recent satellite observations, however, have provided ample evidence of the important role played in magnetic reconnection by relatively cold ions of ionospheric origin, such as oxygen (O+) ions. By conducting global three-dimensional simulations, we account for full-orbit dynamics of both solar wind protons and oxygen ions of ionospheric origin and show that intense flows of O+ from the top of the ionosphere may modify and disrupt the near-Earth magnetotail. In these simulations, we demonstrate the ability of oxygen ions to induce "magnetic flux ropes" (bundles of magnetic field lines of the same direction), confined to the duskside of the magnetotail, in agreement with observations. Physical effects responsible for the formation of these fundamental signatures of magnetic reconnection in the magnetotail are crucial to understanding and forecasting space weather.