  We present a thorough analysis of the interplay of magnetic moment and the
Jahn-Teller effect in the $\Gamma_8$ cubic multiplet. We find that in the
presence of dynamical Jahn-Teller effect, the Zeeman interaction remains
isotropic, whereas the $g$ and $G$ factors can change their signs. The static
Jahn-Teller distortion also can change the sign of these $g$ factors as well as
the nature of the magnetic anisotropy. Combining the theory with
state-of-the-art {\it ab initio} calculations, we analyzed the magnetic
properties of Np$^{4+}$ and Ir$^{4+}$ impurity ions in cubic environment. The
calculated $g$ factors of Np$^{4+}$ impurity agree well with experimental data.
The {\it ab initio} calculation predicts strong Jahn-Teller effect in Ir$^{4+}$
ion in cubic environment and the strong vibronic reduction of $g$ and $G$
factors.
