It's all about the test case.
This is what you really care about. What am I testing, and what's the result of the test? When you create a test case, you can choose to assign it to any member of your team. When that assignment is made, an email is sent to that person letting her know that she has a new test case to be tested. When she logs in, she'll see that test case in her Test Cases section below the project list. When she runs the test case and logs the results from this page, those results will be emailed to you and show up in the project overview.
In the unlikely event that the test case fails (your stuff always works, right?), then the option to create an issue will be presented and a new issue will be created as the next step in the process. Just like a test case assignment, users who are assigned to issues will have email notifications about the assignment, and the reporter of the issue will get email updates as changes are made to the issue.