Here are a few comments about what I guess it might mean if it is a Buddhist point of view.
The first is that Buddhism distinguishes like a rainbow or spectrum of mental phenomena, which occur one after the other, for example:
- The sense bases -- for example skin and the sense of touch
- Contact -- between objects and the senses and the mind
- Feeling -- the sensation or assessment that a contact is pleasant or unpleasant or neutral
- Craving -- for continued (or for discontinued) contact and feeling
I think the view (Buddhist doctrine) might be that these (these events or mind-moments) happen one after another, and that you're not aware of them all simultaneously. For example first there's contact (e.g. between the mind and the sense of touch), and then there's feeling (e.g. "that feels nice" or "that feels painful"), and then there's craving (e.g. "I wish that would continue" or "I wish that would stop").
Maybe a theory is that by the time you develop a "feeling" or "craving", then the "sensation" which caused it is already in the past. At the moment when you have a "sensation" you haven't developed a "feeling" or a "craving" about it.
The second is that her quote says to "localise" the pain: which might be important.
If you don't localise the pain then you might think, "that's pain, I am hurt". If you localise it then you might think, "Pain ... in the hand ... in one small part of the right hand." Localizing it to one spot might be already better then feeling as if it had hurt all of you. It might also make you aware of other parts which are or aren't also hurt. If you're also aware of other parts, then your awareness of the localized hurt part might be intermittent (assuming it's true that you can only be aware of one part at a time).
As an exercise, now try touching two fingers or two thumbs (on two different hands), and try to be aware of the sense of touch on both fingers. You might find that your awareness switches rapidly from one finger to another and back again: you're not continuously or solidly aware of both.
This exercise might demonstrate an example of discontinuous awareness of physical sensation: i.e. that it happens in the past or future but not exactly right now (instead it comes and goes several times per second).
The above are small time scales (e.g. one second, more or less).
The general statement might be also true (be meaningful/applicable) over much longer time-scales: if e.g. pain hurts today I might worry that it will get worse tomorrow, or next year; or maybe it doesn't hurt much today but I remember it used to hurt.
Lastly there's a Buddhist aphorism, that "This is not mine, this is not I, this is not my self."
Having "a view of self" apparently makes things worse: a thought like "I am hurt" increases suffering.
If instead you avoid that view (of self), perhaps that's a kind of emptiness which she seems to hint at when she says, "you begin to see that there isn't anything in between".
Phenomena are maybe transient, distant, and/or localized, passing, past, or future (not present).
See e.g. this essay about Emptiness (emptiness is an important part of Buddhist doctrine).
Another important Buddhist view is that things are impermanent. Whatever they are, they come and go, they arise and cease, they change and change again. In that way, things tend to be past or future.
Related to that, I think that a view like "that is pain" is a mental categorization. The experience which it's categorizing might be already past, or just about to happen (or not just about to happen).
My guess from Byron Katie's Wikipedia page is that she might encourage you to experiment (or "play") with alternative categorizations like, I don't know, maybe: what if you don't call it "pain"? what if you concentrate on it? or what if you don't concentrate on it, or concentrate on something or someone else? what if you try to do something about it (seek medical help)? or what if you stop trying to do something about it? etc.