This will perform a disconnect from the VNC server but anything you leavethat is left open within the VNC session continues to run as long as the VNC server is running. To close out of VNC Viewer or Chicken of the VNC, just close the VNC window.
If that doesn't suit you, our users have ranked more than 50 alternatives to TigerVNC and many of them are available for Mac so hopefully you can find a suitable replacement. It's not free, so if you're looking for a free alternative, you could try Chrome Remote Desktop or DWService. The most popular Mac alternative is AnyDesk. There are many alternatives to TigerVNC for Mac if you are looking to replace it.I can say this after delivering VNC based solutions to customers for the last 7 seven years. For many (or even 'most' in my context) customers/cases, the VNC bandwidth requirement is no problem. TurboVNC/TigerVNC (or the Sun or ThinLinc versions of it) wins here.