Since a few days ago, I'm testing a RDS Aurora Writer-Reader (like classic mysql Master-Slave). Specifically in its recovery capacity agains a failover in the writer, among other task, RDS should swap itself the Writer and Reader Role (all good in this step) and swap the endpoint CNAME so that the application can continue normally.
In my case, this final step not happend, and my application still pointing to the same machine (this machine is in failover and then it's degraded to reader).
To test this, I use "Test Failover" button in RDS panel.
The feature of change CNAME endpoint is mentioned in the official docs: https://aws.amazon.com/rds/faqs/#45
In the following paragraph:
Failover is automatically handled by Amazon RDS so that you can resume database operations as quickly as possible without administrative intervention. When failing over, Amazon RDS simply flips the canonical name record (CNAME) for your DB instance to point at the standby, which is in turn promoted to become the new primary. We encourage you to follow best practices and implement database connection retry at the application layer.