I set up my application for TestFlight. For external users it is waiting for review. But if I want to invite internal users, I select them and press invite. iTunes Connects says
This is what worked for me in November 2017.
I'm not sure what triggered the invite email to be sent to internal testers, as there was only a button for external ones, but soon after I did #2, I got an invite as an internal tester.
Also, as I didn't track this process too carefully, I may have triggered the solution by changing the marketing build version in my app submission (#2) to be the same as my beta build version.