The time-dependent Schrödinger equation is not really a heat equation. Still, the Crank–Nicolson method is well suited for its solution. However, the Crank-Nicolson method is fully implicit, so the statement "doing the implicit part with ADI" sounds a bit suspicious. It probably means that the diffusion like part is done with ADI. I wonder a bit whether that means the potential part is treated by an analytical solution together with another application of an operator-split scheme. (But why would we call this a Crank-Nicolson method?)
For the heat equation, normally the ADI methods Peaceman–Rachford, Douglas–Rachford and Douglas–Gunn get discussed. I'm not so sure how much this analysis carries over to fake/formal heat equations, but at least Douglas–Rachford is certainly unsuitable for the Schrödinger equation. There certainly are stable ADI schemes that can be used for the Schrödinger equations (probably Douglas–Gunn works), but an arbitrary ADI scheme that works well for the heat equation is not guaranteed to also work well for the Schrödinger equation. But even if it would be unstable, it would probably be only weakly unstable, so that you should still be able to get "some" results. So really "weird" results probably have a different origin than the stability of the ADI scheme.