Turning off the auto-assign will work on the new instance, but not on the existing instance. To make the changes affects also the existing changes you need to manually remove the public address from them:

1. Stop the Instance:
2. Detach and Reattach the Network Interface
3. Restart the Instance

Also you should not forget to update the launch template if you're using one, and modify the network interface settings to disable “Auto-assign public IP”