The g factors of $11/2^{-}$ isomers in semimagic $^{109}$Sn and $^{111}$Sn (isomeric lifetimes $\tau =2.9\left(3\right)$ ns and $\tau =14.4\left(7\right)$ ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses LaBr$_{3}$ detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, $g(11/2^{-}{;}^{109}\text{Sn})=-0.186\left(8\right)$ and $g(11/2^{-}{;}^{111}\text{Sn})=-0.214\left(4\right)$, are significantly lower in magnitude than those of the $11/2^{-}$ isomers in the heavier isotopes and depart from the value expected for a near pure neutron $h_{11/2}$ configuration. Broken-symmetry density functional theory calculations applied to the sequence of $11/2^{-}$ states reproduce the magnitude and location of this deviation. The $g(11/2^{-})$ values are affected by shape core polarization; the odd $0h_{11/2}$ neutron couples to $J^{\pi }=2^{+},4^{+},6^{+}...$ configurations in the weakly-deformed effective core, causing a decrease in the g-factor magnitudes.