Time Patrol, Emberverse and Genesis

What happens when a time traveler tries to change the course of past events? There are different answers to this question. In Poul Anderson's Time Patrol series, the altered events tend to return to their previous configuration. What happens when a group of people write themselves into a story and turn it towards their own ends? Again:

"'Events try to reshape themselves towards the original ending.'"
-SM Stirling, The Sea Peoples (New York, 2017), Chapter Fifteen, p. 230.

But how can anyone write themselves into a story? This "story" is imagined by a powerful entity, whether divine or demonic, and the characters in the story are self-conscious, like the "emulations" in Anderson's Genesis. Thus, some imaginative concepts are common to the Time Patrol, the Emberverse and Genesis.