Should @CreationTimestamp make the "created_at" fields of the object being updated after save has been done?

Question

In the @Entity I have a field:

 @CreationTimestamp
    @Column(name = "created_at", updatable = false, nullable = false, columnDefinition = "TIMESTAMP")
    private LocalDateTime createdAt;

in the @Service I have:

 @Transaction
 void someMethod() {
 Entity entity = new Entity();
 entity.setStatus(someStatus);
 entity = entityRepository.save(entity); //here I expect the entity's created_at should be updated
 entity.getCreatedAt(); //here I get the null
 //some other actions
 entityRepository.save(entity);
 }

// finally the created_at is set in the db

Are my expectations correct? Is there a way to get this created_at being saved as it would be stored to the DB?