RDS PostgreSQL minor version upgrade wasn't performed

The reason why your instance was not upgraded to these minor version is that AMVU will only upgrade the enginer version for your RDS instance if the current engine version is being deprecated or the new one contains very important cumulative bug fixes and an upgrade is absolutely necessary.

Please note that while we highly recommend that you perform an upgrade to 10.9, this upgrade will not happen automatically as of now using AMVU as the automatic upgrades happen only when absolutely necessary and you can also view such actions using describe-pending-maintenance-actions command.
Also, I would like you to know that If there is an auto minor version upgrade scheduled as a maintenance, please be assured that you will get a separate notification explicitly mentioning the same. Currently, in this case the upgrade would have to be applied manually.
At your end you can check if the minor version upgrade will happen automatically or not by using the below CLI command:

$aws rds describe-db-engine-versions --output=table --engine postgres --engine-version 10.6

Output:
||-------------------------------------------------------------------------------------------||
||| ValidUpgradeTarget |||
||---------------------------------------------------------------------------------------||
||| AutoUpgrade | Description | Engine | EngineVersion | IsMajorVersionUpgrade |||
||---------------------------------------------------------------------------------------||
||| False | PostgreSQL 10.7-R1 | postgres | 10.7 | False |||
||| False | PostgreSQL 10.9-R1 | postgres | 10.9 | False |||
||| False | PostgreSQL 11.1-R1 | postgres | 11.1 | True |||
||| False | PostgreSQL 11.2-R1 | postgres | 11.2 | True |||
||| False | PostgreSQL 11.4-R1 | postgres | 11.4 | True |||
||---------------------------------------------------------------------------------------||

From 10.6 version, as you can see "AutoUpgrade" column is marked as "False" for all minor version upgrade (either 10.7 or 10.9) . So, it has to be done manually. Please make sure to upgrade to the latest minor version (10.9) so that you wont be prone to any security vulnerabilities as per the following notice:

[+] https://www.postgresql.org/about/news/1949/

In order to apply the minor version upgrade to 10.9 manually, please refer to the below link:
Upgrading the PostgreSQL DB Engine for Amazon RDS:
[+] https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_UpgradeDBInstance.PostgreSQL.html

Let us know if you need further information

Thank you for the detailed answer.