I don't have any experience with Webuzo, but quite a bit with DirectAdmin (another control panel). Editing something directly on the server is never a good idea, the control panel will in fact rewrite its configurations from its own stock on every change.
Regarding Nginx, Webuzo should take care of that for you and you won't need to edit anything to get multiple sites working. If it doesn't, something in their implementation of Nginx seems to be off. Because then it's not just Laravel, but all sites.