When I pushed a branch to my remote on github it was giving me the message:
remote: Create a pull request for \'branch-name\' on GitHub by visiting:
remote:
This is fairly recent (sept. 2018) and is described as:
When you push a new branch to GitHub from the command line, you’ll now notice a URL within the output which you can copy in order to quickly open a new pull request.
So this is when you are pushing a new branch, not when you are pushing new commits to an existing branch.