Exactly, only TotalMix FX "Full mode" (vs. DAW mode) gives you the best flexibility.

In Full mode every HW output (bottom row) has its individual submix.

Full mode is easiest to operate in the so-called "submix mode" (vs. free mode).

In submix mode you only need to click on an HW output, and then the fader position of
- HW inputs (top row) and
- SW playbacks (middle row)
show you which channels are being routed into the selected HW output.

To check the routing of each output (aka "submix", hence the name "submix mode"), you only need to click on them one by one to observe the fader positions of the top and middle rows.
With the button "sub" on the right side, you can toggle the view to show only those channels that route audio into the selected output (submix).

The middle row acts like a patch bay. Audio from the computer is not directly sent to the real HW outputs (bottom row)
but to the SW playback channels (middle row).

This gives the ultimate flexibility for each HW output to route audio
- from HW inputs with near-zero latency (as the routing happens directly on the interface without the transport over USB) and
- from SW playbacks (with the usual latency over USB, which depends additionally on the configured buffer size for the transfer)

I organize audio on my computer so that I send audio from the operating system and different applications to individual outputs.
Also, audio from the DAW can be sent to different outputs to split the different tracks, subgroups.
Then these different audio streams from the computer show up in the middle row under SW playbacks.
I split this up to a level that it is most useful for creating monitor mixes (for monitors and one or more headphones).

I am using the following output channels of the HDSPe MADI FX for these different purposes:
SW Playback AES 1/2: Audio from the OS (Windows default sound device for OS and applications without ASIO support)
SW Playback PH1/2: Audio from MusicBee Player
SW Playback MA1/2: Games (some games support output on a different channel than the default windows sound device)
SW Playback MA3/4: SGear1, virtual guitar amp (standalone mode) for 1st guitar player
SW Playback MA5/6: SGear2, virtual guitar amp (standalone mode) for 2nd guitar player
SW Playback MA7/8: Lexicon PCM81, external FX
SW Playback MA9/10: Lexicon PCM91, external FX
SW Playback MA11/12: DAW Sum

you can even breakup audio from the DAW a little more to have more flexibility for creating monitor submixes for every band member by using for example these additional outputs:
SW Playback MA11/12: DAW Track of Solo Guitar #1
SW Playback MA13/14: DAW Track of Solo Guitar #2
SW Playback MA15/16: DAW Track of Rhythm Guitar #1
SW Playback MA17/18: DAW Track of Rhythm Guitar #2
SW Playback MA19/20: DAW submix for Drums
SW Playback MA21/22: DAW Track of Bass
SW Playback MA23/24: DAW Track of Keyboard
SW Playback MA25/26: DAW Track of Synthesizers
SW Playback MA27/28: DAW Track of Vocals
SW Playback MA29/30: DAW Track of Background Vocals

Even for gaming this splitting of audio channels can be useful.
It allows you to fine tune the monitoring for special situations.
During gaming I am sometimes listening to my own music.
In one special situation I even listened to the audio of a YouTube Video which explained several things about the game.

Using these SW playback channels:
- SW Playback AES 1/2: Audio from the OS/Youtube to listen to game explanations while playing
- SW Playback PH1/2: Audio from MusicBee Player, gives me a little background music for entertainment,
- SW Playback MA1/2: Audio of the Game, turned down a
I could create a perfect submix from these channels to enable listening to the YouTube video while gaming and listening to some music in the background.

Full mode makes it possible to create any submix for every output that is useful for your current use case.
Be it for listening to music, monitoring mixes or for the routing of audio from the DAW to external devices.

Audio from the hardware inputs is always sent unmodified to the application / DAW.
To use the FX of TM FX for recording you have to enable this in the driver settings.

My recommendation for DAW recording is that you record audio unmodified/raw and do the processing later in the DAW.

More information you get via this sticky posting, which gives you an overview and further sources of information:
https://forum.rme-audio.de/viewtopic.php?id=34394