Your outlet tester may do double-duty as a GFCI outlet tester, simulating a ground-fault by the push of a button on it. There is a limitation here. Unlike a good GFI, which can test itself even without a good ground, the three-prong GFI outlet tester depends on a good ground to purposely trip the GFI; and this is also true when it is used to try tripping the GFI by pushing the tester's button at standard receptacles wired downstream from it.
If one doesn't trust the test button on the GFI, and one knows the outlet tester can give a false negative in this scenario, how does one verify the circuit protection?