In the context of the search for electric dipole moments, a proper theory describing frequency shifts for particles precessing in traps is needed to evaluate the systematic effects. We present here such a theory, valid in the ballistic regime and in the nonadiabatic limit. It permits the calculation of the frequency shifts for arbitrary geometry of the confinement cell as well as for arbitrary shape of the magnetic field, such as those induced by localized magnetic impurities. Our improved theory is especially relevant for experiments measuring the neutron electric dipole moment with an atomic magnetometer. Indeed, the main systematic effects of performed, on-going and future experiments can be assessed with increased confidence and precision.