Edit I think the process attribute must point to an element in the same a4j:form. You can skip to my answer below.
Reading the Using process attribute section of this article they mention that it can point to any container. What tags qualify as a container for use of the process attribute? Some that I am specifically considering:
- a4j:form
- a4j:outputPanel
- a4j:region
- rich:dataTable
- rich:panel
- rich:modalPanel