We study exciton spin decay in the regime of strong electron-hole exchange interaction, which occurs in a wide variety of semiconductor nanostructures. In this regime the electron spin precession is restricted within a sector formed by the external magnetic field and the effective exchange fields triggered by random spin flips of the hole. Using Hanle effect measurements, we demonstrate that this mechanism dominates our experiments in CdTe/(Cd,Mg)Te quantum wells. We present calculations that provide a consistent description of the experimental results, which is supported by independent measurements of the parameters entering the model.