I have created a new Shell configuration:

When I start the session, Terminus does not correctly change the directory to what is define in the Shell profile:

This is with Alpha 106 on a Windows 10 box.
I also could not get this feature to work. Likewise, when the feature is turned off, new tabs are not created in the previous directory.
I also have multiple hard drives if this changes anything.
The Cygwin label might be misleading. I think it affects all shell types.
For Cygwin, it seems a viable workaround is to simply define HOME with the appropriate path in the environment settings of the configuration.
The same workaround seems to be good for WSL (WSL 1, I do not use WSL 2)
Most helpful comment
For Cygwin, it seems a viable workaround is to simply define HOME with the appropriate path in the environment settings of the configuration.
The same workaround seems to be good for WSL (WSL 1, I do not use WSL 2)