The evolution of Europa's water-product exosphere over its 85-h day, based on current models, has not been shown to exhibit any diurnal asymmetries. Here we simulate Europa's exosphere using a 3-D Monte Carlo routine including, for the first time, the role of Europa's rotation on the evolution of exospheric molecules tracked throughout the orbit. In this work we focus on understanding the behavior of a single atmospheric constituent, O2, sputtered by a trailing hemisphere source with a temperature-dependence under isotropic plasma conditions. Under rotation, the O2 is also subject to the centrifugal and Coriolis forces in addition to the standard gravitational forces by Jupiter and Europa in our model. We find that the O2 component, while global, is not homogeneous in Europa local time. Rather, the O2 consistently accumulates along the direction of Europa's rotation at the dusk hemisphere. When rotation is explicitly excluded in our simulations, no diurnal asymmetries exist, and any accumulation is due to the prescribed geometry of the sputtering source. We find that the assumed thermal-dependence on the O2 source is critical for a diurnal asymmetry: the diurnal surface temperature profile is imprinted on to the near-surface O2 atmosphere, due to small hop times for the non-adsorbing O2, which then effectively rotates with Europa as subsequently described in Oza et al., 2018; Johnson et al., 2019. Simulation tests demonstrate that the diurnal asymmetry is not driven by the thermal inertia of the ice, found to have only a weak dependence (< 7%). Altogether, the various test cases presented in this work conclude that the dusk-over-dawn asymmetry is driven by Europa's day-night O2 cycle synchronized with Europa's orbital period based on our model assumptions on O2 production and loss. This conclusion is in agreement with the recent understanding that a non-adsorbing, rotating O2 source peaking at noon will naturally accumulate from dawn-to-dusk, should the O2 lifetime be sufficiently long compared to the orbital period. Lastly we compare hemispherically-averaged dusk-over-dawn ratios to the recently observed oxygen emission data by the Hubble Space Telescope. We find that while the simulations are globally consistent with brighter oxygen emission at dusk than at dawn, the orbital evolution of the asymmetries in our simulations can be improved by ameliorating the O2 source & loss rates, and possibly adsorption onto the regolith.