Like most time travel paradoxes in fiction, they are initialized by the author of the screenplay.
An actual predestination paradox would require either that
1. the characters have no free will (i.e., they are helpless to do anything other than fulfilling their own destiny, either through ignorance or an external force of Fate controlling their actions or circumstances), or
2. the result of the paradox is something desirable that, even with free will, the character chooses to carry out (e.g., the character in "Predestination" learns that he was born only as a result of the paradox, so he makes a point of sustaining the paradox to ensure that he will have been born).
This movie seems to be a combination of the two, with the younger character being ignorant of the paradox, and the older character actively perpetuating the paradox.
The problem is that the characters in this movie work for a time travel agency unrelated to the paradox. 999
Presumably the function of time cops is to go back in time and alter the past, or prevent the past from being altered. But in a story primarily about a predestination causality loop, the existence of other time travelers actively trying to change history seems incongruous with the premise of the paradox. How can the same time machine be used both to change history, and at the same time perpetuate a self-recursive predestination paradox?
(Or, if every use of the time machine results in a predestination paradox, how long would it take the time cops to realize that they are completely ineffectual, going back in time only to do what was already done in the first place? Like <PERSON> causing the existence of <PERSON> by trying to prevent his existence in the first "Terminator.")
The movie also doesn't address what would happen if the character did have free will and chose not to continue the causality loop after becoming aware of it (e.g., what if he killed his younger self instead of his older self? With one decision, he could have gone from a predestination paradox to a grandfather paradox.). 45