You've already taken the first step by compiling the automation libraries into your tiles. The next step to automate a complete mosaic application is to install and use the mosaic-debug-auto-pkg.zip which has the automation also compiled into the mosaic runtime. This package is not currently available publicly on packageshare for a couple of reasons: a) a bug in gravity (CCF) and b) a limitation in the flex sdk. The bug in gravity has been fixed and will be released shortly in an upcoming service pack. The flex sdk limitation is here: https://bugs.adobe.com/jira/browse/FLEXENT-1496 I believe the mosaic automation package will remain a special-request package even after the release of the service pack due to the complexity of automating a modular composite application.
Another technique you can consider is to use Selenium with an html controller tile. The html controller would use mosaic apis to send events and messages to the other tiles in the applicaiton. The individual tiles would be automated seperately for UI inputs, and then the system-level automation could use the selenium approach. This can be a simpler and more economical option, depending on your application's design and verification needs.