I've asked some other dev from another project who is more familiar with Transifex. IIRC the had some automatism in the past, which is abandoned now.
There is a tool called Transifex Client ("tx"), which acts like a VCS for Transifex. In my understanding it works like this:
1. get the source from github
git clone https://github.com/RuneAudio/RuneUI
2. connect the language files with the tx client to the transifex project and upload them
cd RuneUI
tx init
tx set --auto-local -r runeadio.runeui 'languages/<lang>.php' --source-lang en
tx push -s -t
3. people can translate everything on the transifex website
4. use tx to pull the changes to your local git repo and commit them to github:
tx pull -a
git add *.po
git commit
