I'm not saying my approach is correct, keep that in mind.

I care more about the code than the tests. Tests are verification of my work. And yes, there is a risk of AI "navigating around" bugs, but I found that a lot of the time AI will actually spot a bug and suggest a fix. I also review each line to look for improvements.

Edit: to answer your question, I will typically ask it to test a specific test case or few test cases. Very rarely will I ask it to "add tests everywhere". Yes, these tests frequently fail and the agent will fix on 2nd+ iteration after it runs the tests.

One more thing to add is that a lot of the time agent will add a "dummy" test. I don't really accept those for coverage's sake.