Imagine having to decide whether to restore or evacuate from the view of the characters in the game. Disregard your meta-game knowledge as the player. You are The Kid and you have to make the decision.
The question that arises is if the events leading up to the calamity will repeat themselves after the Bastion resets time. If that turns out to be true, then it's also possible the events after the calamity will occur exactly the same as before, including using the Bastion to restart time, creating a never-ending time loop.
Now let's look at taking the option to evacuate. If the fear of restoring time is that your actions after the time restore are pre-determined, then choosing to evacuate means one of two things. Either 1) you DO have free-will to make changes in each time-loop, as evident by the fact you chose to evacuate in this time-loop, OR 2) you never used the Bastion to restore time; choosing to evacuate is the one and only decision you made with the Bastion core.
But you have the option to evacuate, maybe you have free will to change your decision in the next time loop, right? Well, if this is the rhetoric used to justify using the Bastion to restore time this time, how do you know it won't be used to justify restoring time, every time?
So if you use the Bastion to restore time once, you risk being caught in a time loop, restoring time every time.
If you choose to evacuate, your fears of a predetermined calamity are false, or you never even tried.