  Characterizing non-local magnetic fluctuations in materials with strong
electronic Coulomb interactions remains one of the major outstanding challenges
of modern condensed matter theory. In this work we address the spatial symmetry
and orbital structure of magnetic fluctuations in perovskite materials. To this
aim, we develop a consistent multi-orbital diagrammatic extension of dynamical
mean field theory, which we apply to an anisotropic three-orbital model of
cubic $t_{2g}$ symmetry. We find that the form of spatial spin fluctuations is
governed by the local Hund's coupling. For small values of the coupling,
magnetic fluctuations are anisotropic in orbital space, which reflects the
symmetry of the considered $t_{2g}$ model. Large Hund's coupling enhances
collective spin excitations, which mixes orbital and spatial degrees of
freedom, and magnetic fluctuations become orbitally isotropic. Remarkably, this
effect can be seen only in two-particle quantities; single-particle observables
remain anisotropic for any value of the Hund's coupling. Importantly, we find
that the orbital isotropy can be induced both, at half-filling and for the case
of $4$ electrons per lattice site, where the magnetic instability is associated
with different, antiferromagnetic and ferromagnetic modes, respectively.
