ExternalContext#redirect() does not redirect to parent directory
A relative redirect URL (i.e. when not starting with / or scheme) is relative to the current request URL (as the enduser sees in browser's address bar). It's not magically relative to the context path in the server side as this information is completely unknown in the client side (you know, a redirect is performed by the webbrowser, not by the webserver).
If you want to redirect relative to the context path, then you should include the context path so that it becomes domain-relative. You can get the context path dynamically via ExternalContext#getRequestContextPath().
ExternalContext ec = FacesContext.getCurrentInstance().getExternalContext();
ec.redirect(ec.getRequestContextPath() + "/" + page1);
In case of page2, the full redirect URL becomes /user/department/newdepartment.jsf and the leading slash / would make it relative to the domain http://localhost:8080, which is exactly what you want.
See also:
- What URL to use to link / navigate to other JSF pages
- Redirect to external URL in JSF
- Hit a bean method and redirect on a GET request
- How to navigate in JSF? How to make URL reflect current page (and not previous one)