DAW mode is the same as in TM FX: Options -> Reset Mix -> Straight playback

From the manual: Straight Playback: All Playback channels are routed 1:1 to the Hardware outputs. The faders in the third row are not changed.

This allows you in submix mode the flexibility to modify the routing of each of the HW outputs individually.
For example, to route directly from a HW input to a HW output without the RTL (round trip latency over USB) in near-realtime.
In pure DAW mode everything has the full RTL over FW/USB/TB ...

Look here:

And external HW (only highlighted in the drawing without detailing the signal flow), you can best integrate through the DAW as external FX device. Cubase has such a possibility, maybe your DAW as well.

You only need to define such a device, input/output ports.
Cubase “pings” through the device to gather delay.
Then you have full latency compensation for it, regardless of the ASIO buffer size, that you use.
You can use it then like a VST as insert or send effect.

Side note: the more channels your recording interface has, the more possibilities you have to create subgroups in your DAW project and to route them to different outputs.
Audio appears then in the middle row SW playbacks, and then it acts like a patch bay to create the perfect individual submix for each of the real HW outputs in the bottom row.

Then even every musician can change his submix with TotalMix Remote over network by using a Windows PC, tablet, convertible, tablet. A drummer wants perhaps to hear more from the bass player or rhythm group, etc.

Creating individual submixes for each of the HW output is far more flexible comparing to routing in the DAW, and you can save/recall your settings easily in TM FX. Furthermore, you can create latency free routings from Mic inputs to phones, directly on the recording interface without having the full RTL (round trip latency) over USB/etc. in the signal path.

This is how I use my outputs:
SW Playback AN 1/2 – Windows OS and applications not supporting ASIO, default sound device in Windows sound settings
SW Playback AN 3/4 – MusicBee Player (has ASIO support), I want this audio separated
SW Playback AN 5/6 – Games (if they support configuration of audio channel)
SW Playback AN 7/8 – currently not yet implemented but in the future I plan to use this for DAW output (stereo sum)
SW Playback ADAT 1..16, MADI 1..64 – different phones outputs or for future demand (subgroups in the DAW to create even more customized monitoring mixes for musicians)

By splitting audio like this and using SW playbacks as "patchbay" I have most flexibility to create submixes as I like.
Even when gaming.
In the output channel for my headphones I can create an individual submix of 3 audio sources
- SW Playback AN 1/2 - e.g. to get information about a game (let's play videos)
- SW Playback AN 3/4 - to add background music from my musicplayer
- SW Playback AN 5/6 - audio from the game
Then I can play relaxed the game, having nice background music and listen to some infos / instructions from Youtube video in the background.

This is the flexibility that I like, and the operation is very logical structured. Once you understand these basic principles, you can do everything …