How can the future both be set in stone and possible to change?

[neatoman]

So this really bothers me. In Tale of the Yokai, all the interactions between the Turtles and the people of the past were implied to be how history had always unfolded, even though the episode just before said Savanti tried to change the past. So far the past has not yet been altered by time travel but for obvious reasons, I think we can assume the turtles will succeed in preventing the black hole generator from destroying the earth.

So how can one episode depict time as always following a certain path while half a season is dedicated to to mission to change the future?