The documentation you link to directly specifies how to connect to an RDS instance via SSH:
http://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/CHAP_MySQL.html#MySQL.Concepts.SSLSupport
mysql -h myinstance.c9akciq32.rds-us-east-1.amazonaws.com \
--ssl-ca=[full path]rds-combined-ca-bundle.pem --ssl-verify-server-cert
So the questions now are:
How to get SequelPro to connect via SSH:
According to the SequelPro documentation, it only can connect via SSH using an SSH tunnel.
So you'll need to connect via SSH from your local computer to an EC2 instance in your VPC. Getting this setup has nothing to do with your RDS instance. Once that connection is established, you would use this tunnel to make a non-SSH connection to your RDS instance.
See: https://sequelpro.com/docs/get-started/get-connected/remote
Connect to RDS from your PHP app:
Similarly, it looks like PHP does not have built-in SSH support for MySQL connections.
There are many QA on Stack Overflow on this topic:
Conclusion
In both accounts, it looks like SSH tunnels is the only way to go. So you either:
- live with the tunnels,
- use standard connection (non-encrypted), or
- use other tools/mechanisms to connect that do support SSH.
