It's fine. Actually, part of the ASIO driver's function is to not have any interferring sounds coming from your Windows or whatever operating system you are running your PC on. That's the reason why it mutes the other sounds that might end up on the recording.

You can, depending on the Software you use, tell the driver to be released as soon as you leave the program you are recording in.

You can check if there is such a function in the program you are using.

Lukas