Antiferromagnetism of equi-atomic single-crystalline NiMn thin film alloys grown on Ni/Cu3Au (001) is probed by means of magneto-optical Kerr effect (MOKE). Thickness-dependent coercivity (HC) enhancement of polar MOKE measurements in NiMn/Ni/Cu3Au(001) shows that ~7 atomic monolayers (MLs) NiMn order antiferromagnetically at room temperature. It is found that NiMn can couple to out-of-plane (OoP) as well as in-plane (IP) magnetized Ni films, the latter stabilized by Co under-layer deposition. The antiferromagnetic (AFM) ordering temperature (TAFM) of NiMn coupled to OoP Ni is found to be much higher (up to 110K difference) than in the IP case, for similar interfacial conditions. This is attributed to a magnetic proximity effect in which the ferromagnetic (FM) layer substantially influences TAFM of the adjacent AFM layer, and can be explained by either (i) a higher interfacial coupling strength and/or (ii) a thermally more stable NiMn spin structure when coupled to Ni magnetized in OoP direction than in IP. An exchange-bias effect could only be observed for the thickest NiMn film studied (35.7 ML); the exchange- bias field is higher in the OoP exchange-coupled system than in the IP one, possibly due to the same reason/s.