To me, the issue here really isn't about linguistic precision or whatever, to me, space and time are the same thing; I find that they are essentially intertwined in a way that they cannot be truly separated. When you talk about "next Tuesday", you mean going from point T to T1. You are traveling through space as "time" passes, so when I think of an event that is moved "up", I see it as something that is farther away. For example, if we have a plane with four dimensions, the fourth dimension contains the actual event, and when it is moved "up", it is moved farther along in the positive direction of the x-y-z axis.
So this is a simple chart of how I see it. The blue bars are the fourth dimension, as you can see they intersect our normal three. The point T is Tuesday (now), and T1 is next Tuesday. Now, if you are at, say, some point M (Monday, right before T), and someone said, "we're moving the event up", then it would go to T1, because it's being pushed up through time, and thus along the axes. When something is "moved back", it's closer to the point of origin, and thus closer to your current point, and thus closer (sooner in time).
I suppose that for me, I tend to see time more spatially... though I see it as an element of a larger spatial object (the fabric of the universe, for instance) and that it moves through that, and in turn we move through that.