Those 3-lamp "magic 8-ball" testers are pretty lame, but in two ways.
- the legends, like "hot-ground reverse" or "no hot". They are more useless than a magic 8-ball, because they are wildly speculating at the most likely (easy) cause in the context of new construction. They are wholly unprepared for the realities of maintaining old wiring, and their wrong guesses will waste hours of your time. The lights themselves can be quite useful, especially if you see them in the shade so you can see if some lights are half glowing. By the way, those should be neon, not LED.
- we're seeing a new generation of those which actually have computers inside, and the computer gets between you and the lights. Good chance those lights are actually LED. Again, the computer is aiming to troubleshoot only the most obvious faults, particularly the ones that arise in new construction - if you have a real stumper, the computer will only mislead you.
Pushing the GFCI test button will cause a small (10ma) amount of leakage between hot and safety ground. Any common 8ma GFCI devices upstream of this point will trip.
If there is no GFCI upstream, the GFCI will not trip because it doesn't exist. The overcurrent protection device (the breaker) will not trip because it isn't a GFCI device and 10ma is not anywhere near an overcurrent.
If the receptacle is not grounded, the upstream GFCI will not trip because the intended 10ma of leakage is going from hot to nowhere. Since current flows in loops, it won't flow. In that case, you test the upstream device using its own button and make sure this outlet loses power.