Custom Exception Strategy class not getting being invoked in a Jetty Inbound Endpoint

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When using a Custom Exception Strategy in a flow with a jetty inbound endpoint as a Message Source, the class is not being invoked (none of the handleException methods are invoked)
However, when changing the endpoint to a HTTP Inbound Endpoint, this works as expected.
Attached to the case you can find a test case in which I'm setting an outbound property to the message in the Custom ES, and I'm expecting it in the result.
I get it when invoking the HTTP endpoint, but the property is missing after invoking the Jetty endpoint.