My money is on it having to do something with the jump and concsiousness. Gaal was partially awake, and Salvor survived the non-linearity she experienced even though she was not sedated.

Opposed to it being pure magic:

my non-book-reader, 21st century minded theory is that it has to do with "quantum consciousness", a fringe idea that tries to combine the wave function collapse + entanglement + the mind-body duality with the hard problem (of explaining consciousness). (which is pseudo for now and thereby "magic" tho)

as the empire has the space jump tech, it already demonstrates their space-time-gravity manipulation capabilities (which requires quantum physics). Apparently, all minds "collapse" (or go into psychosis) due to the non-linearity. (except the two.)

I, in a non-physicist bogus armchair way explain that as a sort of frequency interference between the wave fields of our consciousness and the extreme waves fields (?) created by the space jump.

Gaal and her daughter Salvor's mind does not collapse due to it. Furthermore, their memories' / minds' can apparently even "fold" the space-time (the telepathy and the visions from future / past), just as the ships that can jump (maybe not "just as", but prolly using some similar physics). Therefore, I believe; they possess a certain subconscious capability of "manipulating their mind's quantum field or space/time" (sorry, this is getting out of hand) - (I also think this could at one point partially tie into the luminist reincarnation and the "soul" )

In any case. I think, water peeps are not Gaal's bio parents. I think she was in the womb of someone during an "old-school" analogous jump. I think the ship that carried her bio-mom was escaping something or having certain difficulties and Gaal prenatally or as a baby experienced a jump. But because her mind was not fully developed, she survived it and it altered her brain forever thereby gaining this second nature and somehow past it on. Eventually she somehow ended up in a sci-fi version of a floating cradle in the water planet a la superman. (because the jump was problematic and their ship went down and her parents sent her to the closest planet)

Water planet family is the Kents to Gaal. I call this theory: Gaal Kent, who prenatally (or as a newborn) experienced a jump that altered her brain forever. (And the brains of her offspring). She was always meant to be once in a century level intelligence and inherently curious due to her bio-parents, but this altercation gave her and her future offspring, the ability we talk of + the magic-level intuitions. Or I don't know. Maybe it is just pure magic. But I just can't let it go like that.

I also believe the first missing piece in Hari's puzzle is not Gaal's choices, but the event that Gaal experienced as a baby or unborn. Oh oh! Maybe she was actually on the Invictus as a baby? And her cradle was cryogenic?

more edit: Gaal's coming back to the water planet in cryo-pod was foreshadowing to the past we don't know of yet... My mind just removed a rib and sucking itself off

It's basically magic. Telepathy and prophecy and being able to discern the future with 'math' are used extensively in the books. It's just part of the world.

This isn't our universe. It's an alternative reality with themes that sometimes mirror portion of life on Earth and offer alternative angles to view those themes so that we might think about our own problems in a new way. That's what sci fi is all about.