For entangled solutions of linear and star-branched cis-polyisoprene (PI) chains, rheodielectric tests were conducted to examine the nonequilibrium chain dynamics under steady shear. The PI chains had the type-A dipoles parallel along their backbone, and the observed rheodielectric behavior reflected the dynamics (fluctuation) of the end-to-end vector of the linear chain and/or the star arm in the shear gradient direction. This behavior changed only slightly, in both relaxation time and intensity, with the shear rate γ even in the significantly thinning regime at 1/τ i < γ < 1/τ Rouse , with τ 1 = terminal relaxation time and τ Rouse = Rouse relaxation time for the chain length equilibration. Comparison of the γ-insensitive rheodielectric intensity data and the non-Newtonian viscosity/normal stress data indicated that an isochronal orientational cross-correlation emerged over some number (β) of entanglement segments under fast shear. This result was analyzed on the basis of the molecular picture of dynamic tube dilation (DTD) induced by the convective constraint release (CCR). The analysis suggested β ≅ 1.8 and ≅ 1.2 for the linear and star chains at the largest γ examined. The CCR-DTD picture was consistent also with the observed γ-insensitivity of the rheodielectric relaxation time. Furthermore, the current CCR models for the linear chain were examined for the rheodielectric data. It turned out that the observed γ-insensitivity of the relaxation time was not straightforwardly deduced from the models.