We show the possible existence of a significant axial asymmetry in the reconnection separator at the Jovian magnetopause using first‐principle, physics‐based global simulations. Under eastward interplanetary magnetic field (IMF) conditions near Jupiter's orbit, reconnection occurs at the southern‐dusk and northern magnetopause with large shear angles between the magnetospheric and magnetosheath magnetic fields. When driven by the westward IMF, the reconnection position switches to the northern‐dusk and southern magnetopause. Component reconnection at the southern‐dusk/northern‐dusk magnetopause is associated with the interaction of the IMF with the nearly‐dipolar background fields. Nearly‐antiparallel reconnection near the noon‐midnight plane at the northern/southern magnetopause is related to the dawn‐dusk asymmetric, helical, closed lobe magnetic fields, which is a consequence of significant planetary corotation effects and not expected at Earth. Such configuration is testable as Juno has proceeded its orbit to the high‐altitude cusps and provides new insight into the interpretation of measurements from other rotationally‐driven systems.