The effect of post-annealing gas treatments (pure O₂, pure Ar, and 3% CO in CO₂) on the dc/ac-magnetic and surface electronic properties for spark plasma sintered cubic spinel LiNi_0.5Mn_1.5O₄ (LNMO) has been investigated via dc- and ac-magnetization and core-level x-ray photoemission studies. The dc-magnetic susceptibility measurements show that an O₂ annealing atmosphere results in a magnetic ordering near 118.6 K which persists to comparatively lower temperatures in reducing atmospheres. An enhancement of the effective magnetic moment and decrease in the irreversible magnetization in reducing atmospheres results from the presence of oxygen vacancies. The ac-magnetic susceptibility analysis using the power-law and Vogel-Fulcher law yields the spin relaxation time in the range of 10^-9 s to 10^-10 s and confirms the presence of cluster-spin glass, owing to the competitive antiferromagnetic (AFM) and ferromagnetic (FM) exchange interactions in the compound. These observations are corroborated with the core-level x-ray photoemission spectra showing the mixed valence states of Mn^4+/3+/2+ and Ni^3+/2+ and oxygen vacancies of nearly 10-23% (from O 1 s and cation valence), demonstrating that post-annealing treatments can be utilized as a means to desirably control the magnetic and electronic properties of the material.