Limit runner to specific branch?

Im have two servers (staging/production) each with their own running on the server.

Is there a correct way to setup the runners so that my StagingRunner only deploys from the dev branch, and my ProductionRunner only deploys when something is merged into the master branch?

Right now I have setup the master branch as protected and defined that my ProductionRunner only run with protected branches. However, I would like my dev branch to also be protected so I need to make some changes. I have tried with tags without luck.