Deploy to remote server: Permission denied (publickey)

I am trying to setup a simple CI that will deploy my code to my remote server when I push to my master branch on gitlab.

I have disabled password access in my remote host and only allow public key access.

I have the following .gitlab-ci.yml:

image: node:7.2.1

  - mongo:3.4.0

  - node_modules/

  - test
  - build
  - deploy

  stage: test
  script: echo "Running tests"

  stage: build
  script: echo "Building the app"
    - npm install -g yarn
    - yarn install
    - node ./index.js

  # Install ssh-agent if not already installed, it is required by Docker.
  # (change apt-get to yum if you use a CentOS-based image)
  - 'which ssh-agent || ( apt-get update -y && apt-get install openssh-client -y )'

  # Run ssh-agent (inside the build environment)
  - eval $(ssh-agent -s)

  # Add the SSH key stored in SSH_PRIVATE_KEY variable to the agent store
  - ssh-add <(echo "$SSH_PRIVATE_KEY")

  # For Docker builds disable host key checking. Be aware that by adding that
  # you are suspectible to man-in-the-middle attacks.
  # WARNING: Use this only with the Docker executor, if you use it with shell
  # you will overwrite your user's SSH config.
  - mkdir -p "${HOME}/.ssh"
  - echo "${SSH_HOST_KEY}" > "${HOME}/.ssh/known_hosts"
  - echo "${SSH_PUBLIC_KEY}" > "${HOME}/.ssh/"
#  - '[[ -f /.dockerenv ]] && echo -e "Host *\n\tStrictHostKeyChecking no\n\n" > ~/.ssh/config'
  - apt-get update
  - apt-get -y install rsync

 stage: deploy
   - echo "Deploy to production server"
   - rsync -av --delete MYSITE/
   name: production
 - master

I get the following error:

Permission denied (publickey).

rsync: connection unexpectedly closed (0 bytes received so far) [sender]
rsync error: error in rsync protocol data stream (code 12) at io.c(226) [sender=3.1.1]
ERROR: Build failed: exit code 1

I have added the public key in SSH_PUBLIC_KEY to my remote server’s .ssh/authorized_keys file. I feel like I’m having a fundamental misunderstanding of how gitlab runners work. Is rsync being run by a user other than the one I created the .ssh/ file for?