We present a detailed investigation into the correlations between the magnetic and local structural order of Ga 2 MnCo and three new compositions Al 2 MnCo, Ga 2 MnPd, and Al 2 MnPd, which belong to the composition range with dominant p−d hybridization in the extended Heusler family. Our investigations reveal that such systems do not have a propensity to form in the regular face-centered cubic structure with ferromagnetic ordering as its magnetic ground state. The studied compositions are found to demonstrate a re-entrant cluster-glass state. The absence of any associated structural phase transitions in these compositions is ensured from the heat capacity and temperature-dependent X-ray absorption fine structure (XAFS) spectroscopy measurements. The magnetic susceptibility results demonstrate the formation of macroscopic spin clusters, and XAFS identifies the correlation between spin and lattice degrees of freedom. While the inherent anti-site disorder provides the competing interactions, a complex interaction mechanism between the sp and different d atoms, along with an unusual local lattice disorder in these cubic compounds, may act as precursors for the frozen magnetic state. Additionally, the experimental X-ray absorption near-edge structure reflects the electronic features, which hints toward a stronger p−d hybridization in the systems.