I have a Quantum, but not the full version of Studio One. I use it primarily with Logic Pro X. The overriding principle is that ALL audio routing has to be done in the DAW. This requires a change in workflow, and is a little wonky feeling at first if you’re used to a separate DSP mixer app or digital mixer, but actually makes lots of sense when you get used to it. Especially since all routing can be restored in one shot without having to deal with two completely separate mixers and programs. It saves quite a bit of time when recalling a session.
So in Logic, if I wanted to make a separate headphone mix, I would do it with an auxiliary channel, controlling levels with sends, and then I would set the output of the aux channel to the desired pair of hardware outputs.
When I want to send the main DAW output audio to my dedicated artist headphone amp(s) (by far the easiest way to monitor while recording), I use the Logic I/O insert plugin at the end of the master bus to route audio to the outputs feeding the headphone amp. The I/O plugin allows a wet/dry mix, so I don’t have to silence the main output (1-2) that feeds my monitors. Of course, using a dedicated monitoring controller would render this software workaround unnecessary.