To discuss the "rate" of time has issues with self-reference and circular reasoning.
Again -- I just want to make sure there's no confusion -- this is exactly why we're talking about "relative" time -- the comparision between two different rates. This is what this topic is about, so the label of "rate of time" is appropriate here. He's asking about Bionicle's time compared to ours. 
Time itself does not actually move from a purely objective (transtemporal) perspective, but the importance of "rate" remains nonetheless. I often describe time with the metaphor of an old-fashioned film reel. From a transtemporal perspective -- outside of time, or in this case a human looking at the reel -- you can see all the slides at once.
In this case, it would be like looking at two different reels and seeing that in one, the slides are compressed lengthwise. On the other, the slides seem stretched out. If you played the two side-by-side with the same equipment, you'd go through the shorter slides faster than the other. (Nevermind that this analogy kinds breaks down here because if you took it literally the compressed one wouldn't really play properly. 
) If the characters in one film could see the other film and comment on it they would say it is going slower or faster. That's because they're in a temporal perspective.
Yet from your transtemporal perspective (this is the part you are talking about) time really doesn't "move" really. That's true, but irrelevant to what we're talking about here. It doesn't change the fact that time in Bionicle could go faster or slower than "ours" (fictional version of ours) if it existed in relation to Bionicle's dimension.
So to rephrase my earlier questions, how can we know whether time is truly moving "faster" or that everything in that universe is moving faster?
This is an irrelevant semantics question, ultimately, since we simply define "time" in this context as "everything's overall rate". The point is that it's not the same as normal concepts of speed in which for example your atoms will still spin normally even though a car goes faster, etc. When we say that "time goes faster" we simply mean that absolutely everything in that area is affected.
If you're asking if we know whether time really is a "substance", that's beyond my pay grade. Although I've got (and have heard) a lot of theories on it that say yes and no, and the one I lean towards is both yes and no -- that the whole concept of a "thing" can be transcended when you get so basic as to consider spacetime and quantum mechanics, etc., yet the patterns of physics still exist regardless of what labels you put on them or how they are generated, so they're still real.
My answer is that the distinction between the two has no physical meaning.
This is true only for an observer in (and of) only his own reference frame. As soon as you can observe other reference frames (and really this is a gradient effect so there's no smooth boundaries of it; it fades and grows the faster/more-gravity you get), it has physical meaning. As seen in GPS, etc. It also causes redshifts in light which is important in a lot of ways, such as your weather forecaster relying on the Doppler effect that this causes to tell you whether it's going to rain or not, etc.
And anyways, what I'm trying to get across is that it is the view you're putting forward that really has no physical meaning of any importance, so it isn't of any help to dispute the use of the term. See below.
We can use this same principle to address what's going on with the Vahi. If we look at the classic scene where Vakama slows down time in the second movie to stop the shadow hand from killing him, giving Lhikan enough time to save his life, the natural instinct is to say that the Vahi slowed down time.
No, it's canon fact. It made time in one area slower than the surrounding (observing) areas. Or, from Vakama's point of view, time outside him and the hand was moving faster. This had the important physical effect of giving Lhikan enough time to get up there as you say. So what would be the point in debating this? Can you imagine as Lhikan is dying, he says, "Vakama, remember, this is very important... you didn't really slow down time..."? Of course not. Because he did. To say otherwise has no practical value. (Nor backing in physics either.)
The point is, it isn't we fans making some sort of faulty assumption in saying the Mask of Time controls time. That is what the story team says it does (as the name implies 
), and it's their universe, so it does, period.
In response, I would pose the following question: Would the mask achieve the same effect if everything (every object, every atom, every physical process) in the Vahi's range of power moved at a slower speed than before?
But you say that as if that isn't what it does. That's exactly what it does. That's "time."
We are made out of "everything", and parts of "everything" are all we have to measure anything. We have no means to directly measure spacetime other than parts of "everything." So no, we can't be sure our theories of spacetime are quite correct, but that basically becomes irrelevant, because any alternative has to be an untestable hypothesis (or as I call it, a "patch"; which is essentially what Occam's Razor seeks to cut away, the problem with it being that you could come up with a patch to make anything seem to fit anything).
And since "time" is just an English word anyways, we're in charge of what we apply it to, and we apply it to the rate of motion of "everything". This is what it has always meant in English, long before Einstein; he didn't invent the idea.
Basically, you're inventing an idea, defining it in a way that makes it untestable, and asking if it might be real, knowing that we can't answer it -- what's the point? More importantly, why do this only for time? Why not ask whether Tahu is really a Toa, or a Matoran who experiences illusions that he's a Toa and so does everybody else, etc. Basically, why do people seek to come up with these pointless alternatives only when time and similar physics things are in view, yet normally we simply take for granted that what is canon is canon? I suggest that it is only because to you, time does not seem as easy to understand, just 'cuz you're not used to it.
When you do get used to it as I am, it is just as strange to suggest that the Mask of Time doesn't control time as it would be to suggest that Kopaka isn't really shooting beams of ice but is shooting a hologram that perfectly imitates ice in absolutely every way and never lets up.
Does this help?
keep in mind that just because someone doesn't offer particular knowledge in their post doesn't mean they need a full blown lecture on how it works
I had a feeling you understood more than you conveyed, but I've learned from experience that for the sake of others reading along who might not know all of what we physics geeks think of as basics, its best to introduce the basics in plain language each time they are discussed. And I'm still not sure you've quite caught that temporal relativity is the subject of this topic -- specifically, the relative rate of time in one frame compared to another. So for any posts to be on topic here they must discuss this. Your post appeared to miss that. (But ah well, it happens. )
To use another analogy, it's like size. We do not need to know how tall a Toa "really" is in order to know that a Toa is taller than a Matoran. Right? Similarly, two different dimensions (or areas) can have different rates of time. Simple.
