With RDS postgresql upgrade either minor or major you have to bear downtime during the upgrade process (even if you have multi AZ enabled).
1.In background RDS by default will make a snapshot before upgrade (old version)
2. Upgrade will happen at postgresql binaries
3. Security patches will be applied if any
4. Post upgrade snapshot (new version).
5. Instance will be available for connection
Note: it’s best to make your manual snapshot before upgrade, test your application by upgrading development instance first and after testing do it in prod.
Without testing don’t do major upgrades with simple clicks in RDS.
Avg upgrade time will be 40 min based on your instance load it may vary.