We infer the most relevant local magnetic properties of different iron-coated tips by comparing atomic scale contrasts obtained by magnetic exchange force microscopy utilizing the well-known structural, chemical, and magnetic configurations of NiO(001). Tips with only a single magnetic atom at the apex reflect the genuine antiferromagnetic structure of the nickel atoms, while for magnetic double tips an apparent magnetic contrast on oxygen atoms is observed. Furthermore, we found that even large external flux densities are not sufficient to fully align all magnetic moments of the tip and that local reconfigurations at the apex strongly influence magnitude and direction of the magnetic moments of the foremost tip atom. Knowing what kind of processes take place at tip apices will help to understand and tailor magnetic-sensitive tips for scanning probe techniques.