The InvokerRunsPublisher is currently only considering the run goal of the Invoker Plugin in order to launch the MavenInvokerRecorder. However, integration tests with the Invoker Plugin can also be launched with the integration-test goal, and later verified independently with the verify goal. (This is for example the current setup used by Maven team.) In this case, the current publisher will not do anything.
Therefore, support should be added for this goal. I'm not sure if it should/can be checked whether both integration-test and verify have ran during the build for the same project/module. I think only adding integration-test here is enough.