Ni/Cu(100) films are known to exhibit an 'inverse' spin reorientation transition (SRT). The magnetization rotates from in-plane to out-of-plane upon increasing the thickness. The driving force of this phenomenon is a volume uniaxial anisotropy due to the tetragonal film structure, which favours an out-of-plane orientation. We investigated the structure and magnetism of Ni xMn1-x alloys on Cu(100). We find an improved growth of NixMn1-x alloy films compared to Ni/Cu(100). The SRT of NixMn1-x alloy films is studied using the magnetooptical Kerr effect (MOKE). We find that a Ni-type reorientation can be observed for Mn contents up to 13%. For two concentrations, we were able to determine the volume anisotropy KV and surface anisotropy KS values using hard axis magnetization curves, which we discuss in the context of experimentally determined Ni/Cu(100) anisotropy values. We find that the driving force of the reorientation is a positive KV due to a tetragonal distortion. The positive value of KV can be related to the magneto-elastic properties although the variation of the reorientation thickness dc as a function of Mn concentration fails within this model.