Usually, no. A flash like the Godox Lux Master is a simple non-TTL/manual-style flash, so it typically does not communicate with the camera the way a dedicated brand-specific TTL flash does. That means the camera often will not automatically change to a flash shutter speed such as 1/60s just because the flash is attached or firing.

In Auto mode on the flash, the flash is controlling its own output using its sensor, not telling the camera what shutter speed or aperture to use. You normally need to set the camera exposure yourself within the camera’s flash sync limit, then choose the aperture/ISO recommended for the flash’s Auto setting.

If you want the camera to automatically manage flash exposure behavior, that usually requires a dedicated TTL-compatible flash matched to your camera system.