I finally have figured this out:
The problem is when having the vaadin-cdi.jar inside the EAR/lib, its containing ServletContextListener (com.vaadin.cdi.internal.ContextDeployer) is not executed automatically.
The solution is very simple: Just create a web.xml inside the WAR/WEB-INF folder and add an entry:
<listener>
<listener-class>com.vaadin.cdi.internal.ContextDeployer</listener-class>
</listener>
This will make sure, that the @CDIUI annotated class will properly be initialized.