No, I don't define Ni in terms specifically of "the future" anymore; and yes, Berens is one who really pushes the whole "future" focus. (I thought I had remembered you being somewhat generally critical of her presentation of the concepts). Of course, it does often come in handy for getting a sense of the future, (but then so is Ne; the difference, that the latter is not as "sure" about it).
I've since leaned more toward Lenore Thomson's discussion (and an Ni dom. herself).
Descriptions from the chapters on the perception functions (all in terms of what they do wit our "sense impressions"):
Se: "go with our sense impressions as they occur"
Si: "stabilize our sense impressions by integrating them with ones we remember; facts we know to be consistent".
Ne: "unify our sense impressions with their larger context, thereby creating new options for meaning and response"
Ni: "liberate our sense impressions from their larger context, thereby creating more options for perception itself" (The example given is raising the question in one's mind of the possible reasons a suntan is valued by people today, when the original circumstances that gave it its meaning have changed).
Notice, there's nothing about "the future". Especially in discussing something about a suntan, involving the past, rather than the future! When I saw this, and also read other NJ's discuss their perspective, I realized that whole "future" concept was really selling the function short! In our own correspondence, she had described Ni as "looking beyond the map" to get a sense of where something will go. (Where I, with Ne, would be looking at the map and trying to figure something from the objects that are there, including the "larger context" that is visible). That implies the future, but Ni is simply one means of doing that; not itself simply awareness of the future, as "foreseeing" implies. She in the book continues "For INJs, patterns aren't 'out there' in the world, waiting to be discovered [as they are for NPs]. They're part of us—the way we make sense of the rest of the information and energy impinging on our systems".
This really shows what's "introverted" about it, where "foreseeing" in itself doesn't, and leaves you wondering what really makes it different from Ne. (though, again, the process can certainly include foreseeing). This is what I think has kept the meaning of the function so mysterious and hard for everyone to really understand.
Berens herself covers it best in one of the books, when the example of Ni is a person choosing a dog having a "vision" of a dog barking and crying, and then realizing that they should get a dog that didn't mind being alone. This doesn't even have anything to do with any particular singular event being "predicted". It was a subconscious model of a situation that was referenced to inform a decision for the better, to avoid that template possibly being realized in a future event. This is what I was trying to cover through the term “forebodanceâ€. So the "future" in this case is not something certain, being "foreseen", and neither is the negative conotation).