The Test Harness which handles prove t/*.t, counts not only the tests generated by my t/12_exercise_test_sites_method.t script, but also the tests conducted by the module which it calls.

Test::More -- or any test module that relies on Test::Builder -- keeps only one count of tests performed in a particular Perl process. The test testers that ferreira mentioned intercept the output and make the appropriate adjustments to the count for the tests that you are testing.

From experience, I'd suggest looking at several other test modules on CPAN that use either Test::Builder::Tester or Test::Tester and seeing how they structure their tests. That should give you a good idea of what you'll need to do.