The alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method has been introduced to overcome the Courant limit present in the standard FDTD scheme. However, the ADI-FDTD scheme may produce small asymmetries in the field distributions according to the source implementation. In this communication, we compare different source implementation strategies and show that ADI-FDTD scheme has no asymmetry errors up to the numerical noise level, and can be implemented most accurately if the excitation is directly incorporated within the tridiagonal matrix and if the time discretization of the source is done appropriately within each full time step.