f:ajax doesn't obey the 'execute' attribute but always sends all the fields in a form. Mojarra does, however, only process the listed fields as supposed. However, excess fields shouldn't be sent because it increases request size.
<h:inputText id="field1" />
<h:inputText id="field1x" />
<f:ajax execute="field1" />
On button click, both fields are sent (but only field1 would be processed).