Electrical – Connecting 2 GFCI Breakers to 2 Hot Leads and 1 Common

The part where you said they all trip simultaneously and the fact they're all back-to-back makes me suspect of a bad buss bar. Other than that there should not be any correlation between any of these isolated circuits. It's plausible, but highly unlikely the manufacturer shipped out a bad case of breakers and the installer just happened to install them back-to-back but realistically not heard of. Just replace or as Trevor mentioned in his comment swap the known good AFCI with known bad ones and check buss bar for burnt marks. See what happens.

Grounded circuit (green/bare ground wire wired properly):

• Push "Test" on the GFCI protective device, and it trips -> PASS
• Push "Test" on the GFCI protective device, and it does not trip -> FAIL
• Push "Test" on a plug-in GFCI tester, and it trips -> PASS
• Push "Test" on a plug-in GFCI tester, and it does not trip -> FAIL

A fail here indicates the GFCI unit is probably defective.

Ungrounded circuit (green/bare absent or defective):

• Push "Test" on the GFCI protective device, and it trips -> PASS
• Push "Test" on the GFCI protective device, and it does not trip -> FAIL
• Push "Test" on a plug-in GFCI tester, and it trips -> FAIL FAIL FAIL
• Push "Test" on a plug-in GFCI tester at the GFCI receptacle, and it does not trip -> PASS
• Push "Test" on a plug-in GFCI tester at a downstream protected outlet, and it does not trip -> MEANINGLESS

Fail at the GFCI device probably indicates it is defective.

Fail on the plug-in GFCI tester (i.e. it trips!) indicates they have bootlegged ground at the GFCI receptacle- attached the neutral wire to both neutral and ground. It will seem to work at the GFCI, but is still dangerous.

Bootlegging ground at a downstream GFCI receptacle is a mistake, because one of several electrical faults could put 120V on the the grounds, e.g. the cover plate screws or a machine chassis. However this is difficult to detect, since a properly wired downstream receptacle will behave exactly the same way. This means for ungrounded downstream receptacles, plug-in tester testing is completely meaningless.

Once you have settled the question of bootlegged grounds, here's how you test an ungrounded GFCI. Plug your GFCI tester into your handy dandy 2-3 prong "cheater" - the kind with a short green wire as a pigtail. Extend that green wire all the way to a reliable ground source, e.g. the panel in the basement. Now, the GFCI tester should work normally, since you have rigged a proper ground to it.

GFCI protection is pretty effective, and I would be confident in an ungrounded circuit if it has GFCI protection. However if you are unable to get the external device to trip, you'll need to pop the cover off and see if the ground is present, missing or bootlegged.