Yeah, after this chapter I've come to conclude that Alice is the Phantasmal King, when they both talked about the Icarus tales. Firstly Alice talking about the myth on its own, and now the Phantasmal King saying about wings that won't burn even if near the sun. I mean it was kinda of obvious since Alice first appearence, but this just confirms it.
The author just tried throwing a false lead, but "Alice" is a fake identity that while being the King is also a "subordinate" of the King. I'm 98% sure I'm right