We study the Hall effect in NixPt1-x thin films. It is observed that the ordinary Hall coefficient is always negative (electron-like). The anomalous Hall coefficient is also negative, except in the vicinity of the ferromagnetic quantum phase transition, where it exhibits a sign reversal and turns positive (hole-like). This leads to an anti-ordinary Hall effect with opposite signs of ordinary and anomalous contributions. It clearly shows that the anomalous Hall effect does not reflect the overall topology of the Fermi surface (which remains unchanged), but originates from singular hot spots. We attribute the anti-ordinary contribution to the intrinsic (Berry-phase) origin and propose a spectroscopic explanation of its tunability as a function of temperature and composition.