  The Stark-interference technique is commonly used to amplify the feeble
parity-violating signal in atomic experiments. As a result, interpretation of
these experiments in terms of electroweak observables requires knowledge of the
Stark-induced $E1$ transition amplitudes or, equivalently, transition
polarizabilities. While the literature assumes that these transition
polarizabilities do not depend on the nuclear spin, here we prove the contrary.
The nuclear spin dependence arises due to hyperfine mixing of atomic states and
requires a third-order perturbation theory (one hyperfine interaction and two
electric-dipole interactions) treatment. We demonstrate that the so far
neglected {\em tensor} contribution appears in the transition polarizability
and present numerical results for the nuclear-spin-dependent corrections to the
$6S_{1/2}\rightarrow{7S_{1/2}}$ transition polarizability in $^{133}$Cs. We
investigate the effect of these corrections to transition polarizabilities on
the extraction of the $^{133}$Cs anapole moment from the Boulder experiment
[Science 275, 1759 (1997)]. We also consider their effect on the extraction of
the ratio between the scalar and vector transition polarizabilities from the
measurements [Phys. Rev. A 55, 2 (1997)]. While the corrections are minor at
the current level of experimental accuracy, our analysis provides a framework
for future experiments.
