I'm assuming that you are happy with the "trigger" process so I won't consider that
The rest of it
1) in the Build section add a step that will run the unit tests and output in a form that one of the post build actions will understand. For example in python
python setup.py nosetests --with-xunit
2) Add a post build action to publish the results. For example with the command above
add a "publish junit result report" as a post-build action and configure the "Test report XMLs" as "**/nosetests.xml"
There are plenty of ways of doing this but the basic two steps are make the unit tests run and generate some output that one of the report generators understands. Then configure the report generator