Mount EFS to Save Space?

On my EC2, I have mounted an AWS EFS pointing to the Jenkins home directory, /var/lib/jenkins. I did this "with the hope" to stop occupying more space in my /.

What I did was following:

1. I copied /var/lib/jenkins to /tmp
2. I mounted EFS points to /var/lib/jenkins.
3. I copied back all the files from /tmp to/var/lib/jenkins`.
4. I chowned new files that I copied back to jenkins:jenkins.

jenkins runs successfully, and by running df -h, I can see that I am writing new files on EFS (%1). But I also see that I am still occupying more space on / -which is what I wanted to avoid!

I know I am missing something obvious here! but is there any way that I can use EFS without adding more files in / (root folder)?

Thanks,