Metaphysical libertarianism. Yeah, by definition, that's not compatible with the view that everything is determined by physical processes. This is just people freaking out over determinism. I kind of see why. "I am a physical process" sounds like "I am controlled by fate and my choices are pointless". But a person is a process that can't see the future, and a process that experiments and discovers things. Choices are the deterministic process: the person determines things. I could repeat this several times in different words but I'd just be trying to placate a kind of paranoia that happens when people realise they're physical.
Why are you framing this in terms of placating my paranoia? I have no objection to my lack of free will, it does not bother me. It makes me more empathetic to recognize that others lack it as well.