There's an 'objective' timeline, where the past events all happened before the present, and a 'subjective' timeline, which is how Link and you experience the game. Initially, the rule that the game establishes is that the present doesn't change due to manipulation of the past until those manipulations happen in the subjective timeline, after Veran steals Nayru's body and travels to the past to start building the Black Tower. This is reinforced a couple of times as NPCs, and a cutscene in the main story, remark on the sudden appearance and development of the tower. This is also notable in how you can manipulate seeds to grow up specific cliffs by pushing them around.
During the third dungeon arc, however, the Tokay inhabitants of Crescent Island, who mistake Link for one of them, mention how "a Tokay with no tail" opened the mouth of their guardian statue, which is missing an eye in the past, but has it in the present. I suppose it could theoretically have been anyone that did that, but it's suspicious.
Fifth dungeon arc rolls around, and the Gorons mention that Bomb Flowers became their specialty crop after a hero saved the life of their Chief using one... even though Link hasn't actually gotten a Bomb Flower to take back to the past to save the Chief's life yet. When you get the Bomb Flower, the Maku Tree tells you that your name has suddenly appeared in Goron legends where it wasn't before, even though at that time you still haven't yet helped the Chief and become a Goron hero. Meaning that "events that happen in the past objectively are established before they happen subjectively", the exact opposite of how the game's time travel has functioned up to this point.