Correct. In a case of Windows you need to find out option in your player for bypassing system mixer. With Win 10 and above you have an option to use system drivers or install Amanero drivers that gives similar features as with system drivers, plus ASIO output. You can screw up number of things.
In MAC OS bypasing system mixer is not so critical, as sound deterioration is minimal, but if you insist on bit-perfect playback, it was always more tricky. Audirvana could play bit-perfect having two options: 1. Oficially supported, there is a setting in a system multimedia settings app (I hear is not supported anymore) and 2. So called Integer output. The later is a limitation, Audirvana use it as a feature. System mixer require from the application to receive audio stream in the floating point format. When the application is naughty and sends data in integer format, OS recognises "no, its not allowed" and transmit data directly to the driver. But this method never had official support and was broken with some OS updates.
A good practice in both Windows and MAC OS is to not select your DAC as a default playback device. I recommend this setting, as system sound do not mix with the music. I suspect a startup noise on the first computer could be related to this settings.