For entangled solutions of linear and star-branched cis-polyisoprene (PI) chains, rheodi-electric 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)over dot> even in the significantly thinning regime at 1/tau(1) < <(γ)over dot> < 1/tau(Rouse), with tau(1) = terminal relaxation time and tau(Rouse) = Rouse relaxation time for the chain length equilibration. Comparison of the <(γ)over dot>-insensitive rheodielectric intensity data and the non-Newtonian viscosity/normal stress data indicated that an isochronal orientational cross-correlation emerged over some number (beta) 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 beta congruent to 1.8 and congruent to 1.2 for the linear and star chains at the largest <(γ)over dot> examined. The CCR-DTD picture was consistent also with the observed <(γ)over dot>-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)over dot>-insensitivity of the relaxation time was not straightforwardly deduced from the models.