Results of tests is showing on the same SpecRunner.html.
For getting results need to print this loaded page. If html loaded in phantomjs locally, then url should to follow classic Url/Uri rules, especially for a local file (that's why page not loaded):
file:///c:/path/to/the%20file.txt #win
file:///etc/fstab #unix
For getting results of tests need parse logs in after_script in .travis.yml and return value - 0 if tests passed or non-null if tests failed.
Also, probably, it's possible with help itself jasmine (but i'm not sure).