Tropical modes of variability, including the Madden‐Julian Oscillation (MJO) and the El Niño‐Southern Oscillation (ENSO), are challenging to represent in climate models. Previous studies suggest their fundamental dependence on zonal asymmetry, but such dependence is rarely addressed with fully coupled ocean dynamics. This study fills the gap by using fully coupled, idealized Community Earth System Model (CESM) and comparing two nominally ocean-covered configurations with and without a meridional boundary. For the MJO-like intraseasonal mode, its separation from equatorial Kelvin waves and the eastward propagation of its convective and dynamic signals depend on the zonal gradient of the mean state. For the ENSO-like interannual mode, in the absence of the ocean’s meridional boundary, a circum-equatorial dominant mode emerges with distinct ocean dynamics. The interpretation of the dependence of these modes on zonal asymmetry is relevant to their representation in realistic climate models.