Realization of stable spin states in surface-supported magnetic molecules is crucial for their applications in molecular spintronics, memory storage or quantum information processing. In this work, we studied the surface magnetism of dimetallo-azafullerene Tb-2@C79N, showing a broad magnetic hysteresis in a bulk form. Surprisingly, monolayers of Tb-2@C79N exhibited a completely different behavior, with the prevalence of a ground state with antiferromagnetic coupling at low magnetic field and a metamagnetic transition in the magnetic field of 2.5-4 T. Monolayers of Tb-2@C79N were deposited onto Cu(111) and Au(111) by evaporation in ultra-high vacuum conditions, and their topography and electronic structure were characterized by scanning tunneling microscopy and spectroscopy (STM/STS). X-ray photoelectron spectroscopy (XPS), in combination with DFT studies, revealed that the nitrogen atom of the azafullerene cage tends to avoid metallic surfaces. Magnetic properties of the (sub)monolayers were then studied by X-ray magnetic circular dichroism (XMCD) at the Tb-M-4,M-5 absorption edge. While in bulk powder samples Tb-2@C79N behaves as a single-molecule magnet with ferromagnetically coupled magnetic moments and blocking of magnetization at 28 K, its monolayers exhibited a different ground state with antiferromagnetic coupling of Tb magnetic moments. To understand if this unexpected behavior is caused by a strong hybridization of fullerenes with metallic substrates, XMCD measurements were also performed for Tb-2@C79N adsorbed on h-BN|Rh(111) and MgO|Ag(100). The co-existence of two forms of Tb-2@C79N was found on these substrates as well, but magnetization curves showed narrow magnetic hysteresis detectable up to 25 K. The non-magnetic state of Tb-2@C79N in monolayers is assigned to anionic Tb-2@C79N- species with doubly-occupied Tb-Tb bonding orbital and antiferromagnetic coupling of the Tb moments. A charge transfer from the substrate or trapping of secondary electrons are discussed as a plausible origin of these species.