Carbon monoxide (CO) adsorption on ultrathin fcc Fe films is known to result in the rotation of magnetization from out-of-plane to in-plane. By imaging in real time the magnetic domain structure of perpendicularly magnetized Fe/(2 ML)Ni/Cu(100) films during exposure to CO, we demonstrate that the effect of adsorption on the magnetic properties occurs in two distinct stages. Initially, when CO bonds preferentially on bridge sites, perpendicular magnetic anisotropy is enhanced. Later, when on-top adsorption dominates, magnetization rotates towards in-plane in agreement with previous studies. This CO-induced spin reorientation transition (SRT) is not reversible by annealing, as CO desorption would require high temperature cycles which yield permanent structural changes in the metal films. This study demonstrates the existence of a novel non-monotonic behavior of the magnetic anisotropy as a function of adsorbate coverage. The influence of CO on ultrathin film magnetism in real time near critical points, where the anisotropy balance is extremely sensitive to small variations, reveals the previously elusive complexity of this adsorbate induced SRT.