When playing with the Better Combat and First-person Model mods the helmets show up during attack animations. This only happens with armors and helmets from this mod for some reason, others work fine. Playing on Forge 1.19.2, also tested with only those relevant mods enabled.

Mod Versions:
bettercombat-forge-1.7.1+1.19
cloth-config-8.3.103-forge
firstperson-forge-2.2.3-mc1.19.2
immersive_armors-1.5.6+1.19.2-forge
player-animation-lib-forge-1.0.2

Example during sword stab animation:

I've also been having this issue. My guess is that the helmets use special 3d models that First Person Render doesn't know to hide. If you're looking for a band-aid fix you can install Cosmetic Armor Reworked and hide your helmet with it. You won't be able to see the helmet in third person then but you should be able to see when you do those attack animations in first person.