RDS instances do not auto upgrade minor versions

This has been a misunderstood RDS feature for a very long time, and one that still doesn't reflect what many customers expect. While the expectation is that instances with AMVU allowed will be automatically updated to the latest minor version soon after its release, the actual usage is that periodically AWS will decide to apply a minor version to all applicable instances that allow AMVU. So if you want your instances to stay updated with the latest minor version you will need to do it yourself, either manually or with a script you schedule to run periodically.

I see, then it was a misunderstanding on my part.
Is this for minor versions that contain critical fixes, or in what cases does AWS apply updates? I have a hard time finding documentation on the details of this setting.

This is an old post now but I came across it while looking for the answer to this question so I am adding a comment for others as the AWS documentation that I have found is very misleading.

Your instance will only auto-upgrade if there is a version of your database with AutoUpgrade set to true in the output of this command:

aws rds describe-db-engine-versions

The AutoUpgrade value is currently set to false for most database versions and I have not found any documentation that states when these values are set to true but this forum post has a little more information: https://forums.aws.amazon.com/thread.jspa?threadID=306358