Ryujin
Legend
As I see it, an attack that does psychic damage and that has a secondary effect involves the psychic damage acting like a can-opener, to open the way for the after effect. Once you've pried open the opponent's 'head', you're then free to mess around a little. So I guess I'm with WalterKovacs on that; apply damage, but not the riders that would accompany illusion for a creature that has immunity.
Or you take a page out of the errata for resistance and say that unless you have immunity to all applicable keywords, you still take the effects.
Or you take a page out of the errata for resistance and say that unless you have immunity to all applicable keywords, you still take the effects.