It's really easy, you just have to route it properly.
1. Send the mix output to whatever outputs you have hooked to the finalizer inputs
2. Hook the finalizer outputs to a set of inputs on your interface.
3. Turn off ALL monitoring both in logic and hardware monitoring on your interface. (if you don't, you will create a feedback loop)
4. Create a stereo track in Logic and route the inputs to that track.
5. Hit record.
You just need to think it through: You are playing the mix out to the finalizer. (no problem, just route the mix to a set of outputs) You are also recording the output of the finalizer. (no problem, just create a track and route the inputs to it) Normally, you want to hear what you are recording (for monitoring purposes), but in this case you don't want that to happen because it will send the output of the finalizer to the input of the finalizer and cause a feedback loop.