I tried a couple of answers mentioned in this link, but couldn't figure out how to tell Jenkins about the user-selected branch. As mentioned in my previous comment in above thread, I had left the branch selector field empty.
But, during further investigations, I found another way to do the same thing - https://wiki.jenkins-ci.org/display/JENKINS/Git+Parameter+Plugin I found this method was a lot simpler, and had less things to configure!
Here's what I configured -
Added the following values:
Then in the git SCM section of the job I added the same value mentioned in the 'Name' section, as if it were an environment variable. (If you read the help for this git parameter plugin carefully, you will realize this)
After this I just ran the build, chose my branch(Jenkins checks out this branch before building) and it completed the build successfully, AND by choosing the branch that I had specified.