The observed hemispherical power asymmetry in cosmic microwave background radiation may have originated from the modulations of superhorizon long-wavelength modes. In this work, we unveil different aspects of asymmetries generated from the long-wavelength mode modulations. We show that the same mechanism that leads to the observed cosmic microwave background hemispherical power asymmetry via superhorizon long-mode perturbation also yields dipole asymmetry in (a) the tensor perturbations power spectrum and (b) the halo bias parameter. These are different phenomena relevant to different cosmological histories, but both share the same underlying mechanism in generating asymmetries in the sky. We obtain the set of consistency conditions relating the amplitude of dipole asymmetries generated on tensor perturbations and halo bias parameter to the amplitude of dipole asymmetry generated on cosmic microwave background power spectrum. In addition, we show that this mechanism does not produce dipole asymmetry in acceleration expansion in an ΛCDM Universe because the superhorizon curvature perturbation is conserved in this background.