Khuutra is actually right here, for the most part. Zelda director Eiji Aonuma confirmed a while ago that Twilight Princess takes place in the child timeline, where Link and Zelda managed to stop Ganondorf from taking over Hyrule. Hence, the events of adult OoT (by some taken to be the IW) never occured, and that's why so many events from TP play out in parallel with the adult story.
On the other hand, most people I'm familiar with do not consider OoT to be the IW at all - the historical battle, as seen in ALttP, is generally believed to be an event that takes place between TP and ALttP.
But as for the Hero's Spirit (official name), I dunno. He is definitely a Link, but if he's OoT Link or not, we can't know. His clothes are actually quite similar to the Ikanians' from MM, if you care about that sort of thing. I think it is quite symbolic that he is the one who gives Link the ability with which he ultimately defeats Ganondorf, but that doesn't mean he ever fought the man himself - though if he is OoT Link, I'd say that would be likely.
Oh yeah, and the origin of the Hero's tunic is probably magical - it was granted to him by the ToC anyway - so that's not really a problem, since the goddesses would be aware of adult OoT even if it didn't happen in that timeline.
