We investigate the local magnetic susceptibilities of prototypical iron based superconductors. In particular we are interested to understand the impact of strong electronic correlations on the time-resolved dynamics of the local magnetic moment. We therefore study five materials (LaFeAsO, BaFe2As2 , LiFeAs, KFe2As2 , FeTe), all known to be Hunds metals, which strongly differ in their respective degree of correlation. The theoretical calculations are based on ab-initio DFT+DMFT calculations using maximally localized Wannier projections, both on the d as well as the dpmodel. The corresponding interaction parameters have been determined through constraint random phase approximation (cRPA). From our results we are able to identify and explain a material- and therefore correlation- dependent trend of the magnetic susceptibility. Our analysis of the time-resolved spin-correlation function provides the key to qualitatively disentangle different mechanisms governing the local spin dynamics of these systems. Moreover, our findings for the investigated compounds help to understand the origin of the mismatch between inelastic neutron scattering (INS) experiments and the ab-initio theoretical calculations.