We have the same setup, except that you never merge your feature branches anywhere but development. Then dev is merged to staging and deployed for testing and then, when that's all ready to go (potentially after multiple dev->staging merges to fix issues), staging is merged to production and deployed.

It seems really odd to me to branch from master for a feature branch, then push that to master, then push the feature branch to staging, and then push the feature branch to production. Is that what you are doing?