Her ancestors used the ability to bring the fleet. I assume that, like FTL communication in defending Elysium, all the faster than light communications are executed by one person, but they're not actively concentrating on each individual item. Rather, they link their mind with the machine, let the machine do the commands, and let the psionic execute or transfer that information.
M-Bot tells Spensa to teleport them a kilometre south, they teleport one kilometre south. That sort of thing.
Maybe the object to be teleported doesn't even have to be anywhere near the person.
This way, one person could move fleets of starships at any time, anywhere in the universe by the information going through a psionic.
Using a hard drive with psychic abilities, you could easily move a fleet of ships at once, with directions given by someone else. Maybe it's like plugging yourself into satellite 5 from doctor who.