Aurora cluster maintenance window and minor version upgrades

It is indeed a minor version upgrade and if you have "Enable auto minor version upgrade" it should automatically upgrade.

Here are a few helpful hints Automatic minor version upgrade doesn't apply to the following kinds of Aurora MySQL clusters: Multi-master clusters. Clusters that are part of an Aurora global database. Clusters that have cross-Region replicas. If any of the DB instances in a cluster don't have the auto minor version upgrade setting turned on, Aurora doesn't automatically upgrade any of the instances in that cluster. Make sure to keep that setting consistent for all the DB instances in the cluster.

In addition to the above, Aurora's Version Policy documentation regarding AMVU, says "We typically schedule automatic upgrades twice a year for DB clusters that have the Auto minor version upgrade setting set to Yes."

Also, you can check if the version you're running has had automatic upgrades scheduled with this AWS CLI command:

$ aws rds describe-db-engine-versions --output=table --engine aurora-mysql --engine-version 5.7.mysql_aurora.2.09.2

At the point in time I'm writing this, 2.09.2 indeed does not have AMVU enabled yet.

Therefore, I'd recommend that you follow the procedure to upgrade Aurora MySQL by modifying the engine version.