According to Ellone - The Final Fantasy Wiki
Honestly, I don't even remember if this was talked about in-game or not. Of course, this doesn't answer what the origin of her power is, but I thought it was worth posting for people who didn't know the how of it.The Final Fantasy VIII Ultimania explains that Ellone's ability to connect to the mind of another is the same kind of process as when a person junctions a Guardian Force; one's consciousness can't be connected to another without an intermediary with a special ability — a Guardian Force, Ellone herself, or the Junction Machine Ellone.