The Song of Time should be used to control time, as its name implies. But it is really just a game. The Song of Time never was used in OoT to control time. In fact, if I remember correctly, the only one time that the Ocarina was ever used to control time in that game was when Zelda used it at the end, after Link defeated Ganon, to send him back to his childhood. And it was not the Song of Time which she played; it was Zelda's Lullaby.
I believe a lack of another way to control time really gave the developers the oportunity to use the Song of Time to its correct potential. Yes, the Goddess of Time did assist Link and probably gave the Ocarina/Song of Time to do this, though I am not in a position to say who this Goddess is. I would lean towards Nayru, just because she is the only Goddess to have something to do with time in any other Zelda game.