For the record, when you (or maybe just Jung) say 'visually', I I take it that that term refers to ideas, or, as Jung states, archetypes. It is most definitely not referring to literal pictures, just as 'objects' is not referring to words. Such an interpretation is far too rudimentary, and I suspect the reason none of the people you have talked to stated that they think in words is because visual stimuli is so important to our perception of the world that of course would people would identify more with pictures rather than words. Maybe there was a disconnect between your own understanding of the question and how others looked at it?
I cannot really say much on the way Ne perceives and processes information, as I have not put much thought and study into that function, but I have read Jung's own descriptions of Ni multiple times and I think I understand it fairly well. A simple and concise description might be that Ni concerns itself with certain ideas, and how these ideas relate to consciousness. I (recently professed as being a very probable Ni-type, but regardless this remains true as it relates to Jung's descriptions of the functions) recognize this manner of thinking in almost every aspect of my life. Anything I find myself interested in, I find myself more invested in the ideas behind it, the different paradigms and modes of thought within it, the implications and connections it has with other ideas within that discipline and other unrelated ones.
Take three major branches of science: physics, chemistry, and biology (I have always hated chemistry and have developed a hatred of physics, but that is beside the point). Easily the most interesting thing about any of these subjects is how they relate to each other: how physical processes give rise to chemical systems, and how chemical systems and physical interactions develop and maintain 'life'. One can look not only at that, but bring in external and unrelated subjects. One can ponder and observe the philosophical ramifications of, say, a deterministic system giving rise to something that, by all accounts, seems non-deterministic, or similar things of that nature. As to how this mode of thinking correlates to Ni as opposed to Ne, however, I am not so sure. I have no doubt that intuition is a process of relation; that is, how ideas and objects interact with and relate to each other, but my problem is knowing where general intuition ends and where introverted vs extroverted intuition begins.
Obviously, both Ni and Ne deal with the same information, the difference is the libidinal flow of energy in how this information is dealt with. One popular example I have seen for Ne is a single idea which branches out as much as it can, connecting a multitude of ideas which have increasingly little relevance as one explores the novelties of the relations. I either have never seen or don't recall an equivalent for Ni-type thinking, but the implication seems to be that Ne is more expansive whereas Ni is more thorough. Or, to put it a different way, Ne is interested in the number of ideas it can relate to the original idea, and Ni is interested in how the ideas related to the original idea feed into and mold the original idea. For the latter proposition, one may find a decent parallel in quantum mechanics, where an attempt to measure certain properties of a particle change the properties of that particle (I have devoted almost no time into the study of quantum mechanics, and thus have no idea if this is anywhere close to being accurate, so don't quote me on it; it works well enough to illustrate what I am trying to say regardless of its factual accuracy anyway).
I was just telling someone the other day that the primary reason for my interest in history is to observe the ideas and customs adhered to by a particular society in a particular age, but also to see how they have changed over the centuries, and furthermore to be able to apply those ideas into my own mode of thinking, for the sake of having a more complete and balanced holistic picture of humanity and consciousness. Also worth noting, one of the lesser ideas which I have become fixated upon is that of a paradigm of thought or consciousness made up of untold numbers of variables. But I don't care about the paradigm or the values of the variables themselves, I care about how changing any given variable affects the entirety of the paradigm, how one change cascades and affects every other variable in the paradigm, making one small change potentially very effective. There is always this interplay, the idea that everything is connected and everything affects everything else (this is why so much of my thought in recent times focuses on altering perception and patterns of thought). I have come to view this idea as quintessential Ni, or at least NiJe in action.
