staging deploy connected to production database

I'm not sure why but I have both a staging and production deploy using
the 'capistrano/ext/multistage' gem. I set staging to the default:

set :stages, ["staging", "production"]
set :default_stage, "staging"

It deploys correctly to the right path:
#deploy/staging.rb
set :deploy_to, "/home/myuser/public_html/mysite/"

But it connects to the production database not staging database in my
database.yml file:

staging:
  adapter: mysql2
  encoding: utf8
  database: staging_database
  pool: 5
  username: username
  password: password
  socket: /var/run/mysqld/mysqld.sock
  host: host

production:
  adapter: mysql2
  encoding: utf8
  database: production_database
  pool: 5
  username: username
  password: password
  socket: /var/run/mysqld/mysqld.sock
  host: host

Why is it linking to the production database and not staging? I don't
see where that option is specified during the deploy process.

set :rails_env, ‘staging’

set :rails_env, ‘production’

^^ add these in the appropriate files.