GFCI Breaker - Good or Bad?
It depends on the grounding setup.  The pocket tester creates a GFCI fault by using the ground wire.  If ground isn’t wired properly, weird stuff happens.
If ground is present and wired correctly:

the tester will light 2 yellow lights
the GFCI will trip

If ground is absent, and wired correctly (for ground being absent):

The tester will light 1 yellow light
The GFCI will not trip

If ground is illegally BOOTLEGGED to the outlet:

the tester will light 2 yellow lights
The GFCI will not trip

So it sounds like your tester is indicating that some son-of-a-Be-Nice-Policy decided to “bootleg” ground on those receptacles, specifically to fool an inspector running around with a tester.
Bootleg grounds are dangerous setups, and they are more dangerous with GFCI because the GFCI hides their hazard.  If you get between “hot” on that circuit and “bootleg ground” on that circuit, the GFCI will not protect you.