The named creatures, mostly Elementals or Spirits, should therefore not have the psychic immunity.
Fire Elemental, Whirling Spirit, and Grey Wraith.
I was sure that he was, but after looking at the Rules and Code, Codex v2, the FAQ, and a Google search I am not able to find the Psychic Immunity applies to him or Fire Elemental, Whirling Spirit, and Grey Wraith.
Invisible stalker is not a spirit. It is just a force projection.
I assumed it was a force projection based on its "Force" subtype. I assume it is not a straight copy of a D&D monster, and that the name similarity is coincidental. But perhaps that is the explanation.