A direct and element-specific measurement of the local Fe spin moment has been provided by analyzing the Fe 3s core level photoemission spectra in the parent and optimally doped CeFeAsO1-xFx (x = 0, 0.11) and Sr(Fe1 xCox)2As2 (x = 0, 0.10) pnictides. The rapid time scales of the photoemission process allowed the detection of large local spin moments fluctuating on a 10-15 s time scale in the paramagnetic, anti-ferromagnetic and superconducting phases, indicative of the occurrence of ubiquitous strong Hunds magnetic correlations. The magnitude of the spin moment is found to vary significantly among different families, 1.3 muB in CeFeAsO and 2.1 muB in SrFe2As2. Surprisingly, the spin moment is found to decrease considerably in the optimally doped samples, 0.9 muB in CeFeAsO0.89F0.11 and 1.3 muB in Sr(Fe0.9Co0.1)2As2. The strong variation of the spin moment against doping and material type indicates that the spin moments and the motion of itinerant electrons are influenced reciprocally in a self-consistent fashion, reflecting the strong competition between the antiferromagnetic super-exchange interaction among the spin moments and the kinetic energy gain of the itinerant electrons in the presence of a strong Hunds coupling. By describing the evolution of the magnetic correlations concomitant with the appearance of superconductivity, these results constitute a fundamental step toward attaining a correct description of the microscopic mechanisms shaping the electronic properties in the pnictides, including magnetism and high temperature superconductivity.