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Exploring the controllable aspects of local atomic structure and chemical ordering and their correlations with functional properties is crucial for harnessing the potential of complex oxides in the development of advanced materials. In this work, we have investigated the sensitivity of the magnetic properties in a nanostructured metastable spinel compositionally complex oxide (CCO) composition, (Mg0.2⁢Mn0.2⁢Fe0.2⁢Cu0.2⁢Zn0.2)⁢Co2⁢O4, to local chemical segregation and phase evolution introduced through variation in post-processing heat treatment temperature. A combination of x-ray diffraction, scanning transmission electron microscopy with energy dispersive x-ray spectroscopy, first-order reversal curve (FORC) magnetometry, and neutron diffraction and total scattering analyses was employed to understand both average and local structure-property evolution. Structure analysis shows that the postannealing process triggers local and long-range cation diffusion, resulting in changes in the distribution of atoms residing on the tetrahedral and octahedral sites of the spinel structure as well as nanoscale chemical heterogeneity. FORC analysis shows that redistribution of magnetic cations induces subtle magnetic phase separation and soft to hard magnetic phase transformations, and demonstrates incipient demixing of the as-synthesized material well before detection by neutron total scattering. This work additionally highlights the necessity of a combination of advanced characterization techniques for understanding the broader crystal-chemical class of compositionally complex oxides.