A big thank you to all responding. That clarifies a lot.
This is still a complicated matter, yet much clearer now.
There was much useful information to sort through this.
My NI Komplete Audio 6 has a multi client ASIO driver and I have set Windows to non-exclusive mode (should consider to change that for recording, thank you again).
The most useful information was that I should not match formats but have, say, ASIO on my DAW and WAS on Band in a Box.
To quote justanoldmuso: "Hallelujah"