I want to do multiple actions on different managed beans with the same button, one being scoped session and the other request. In my example I use the same bean for both.
That's expected behaviour. The <f:actionListener type>
creates and gets its own bean instance on every declaration. It does not reuse the same session scoped bean which is managed by JSF.
You need to use binding
instead to bind to the already-created session scoped bean instance.
<f:actionListener binding="#{controller}" />