Perhaps the casting of Time Compression has some sort of requirement to be fulfilled that can be only done so by being in the past? Maybe it's more of a ritualistic type of magic, instead of the magic that appears out of thin air like fire and ice? For instance, think of a pentagram that some modern day witches use to cast their spells, they believe it necessary to cast that spell...perhaps one's conciousness must be so far back in time from one's physical self in order to cast the spell? There is no basis, I know, but that's the way I've always seen it.
Yeah, that's generally how I view it. The spell simply had it as a requirement to be in the past, for some magical reason like you give examples of here.

Also, about the whole physical mark that TC leaves on the past, present and future, it doesn't leave one period. The game says that time is set in stone and unchangeable so this means that TC has already left it's mark on the past because it's happening was inevitable due to time being 100% planned out already, but because TC has left it's mark on the past already the people of FF8's past don't notice because that's what time is normally like for them. I'm explaining this a little unclearly but hopefully you understand.
Exactly; time is set in stone, hence TC cannot be a physical process affecting time. As for the marks and all that, it's true that any mark would not be perceived as anything different, because as you say, the marks would always have been there. But what exactly is meant by 'marks' anyway. Sounds a bit too wishy-washy for my tastes but anyway...