The whole point of testing with the test button, is to alert one if the mechanism has got glued up with dust etc, and to test with a meter will alert one if the device has stuck, better than the button, which in general sends more than 30 mA. It does not test speed or ½, full, and 5 times, with positive or negative cycle or a ramp test. Nor are we also testing the back-ground leakage. So also need the clamp-on meter as well.
Since the device can warp as the terminals are torqued up, it needs test after all cables and bus bars are terminated, so without the clamp-on you don't know what it should trip at.
But this is going a bit silly, today we are told no need to do the + and - tests, not sure why? But we don't test a MCB at all, so be it a full-blown RCD tester, a socket tester with a RCD test button, or the built-in test button, it does show likely it will work.
The MK socket the test button must have gone to earth, as pressing it on the 10 mA version would also take out the 30 mA and 100 mA RCDs feeding it. It did show the earth was present, where most the built-in buttons are line to neutral, so even with no earth they would show as OK.
But as to using the machine before using test button or the other way around it makes no never mind.