Exerted attacks and claw weapons

Hello,

I'm currently using infernal cry and using the exerted attacks to trigger fortify/onslaught.

Using two axes correctly expends the exerted charges, and the combust tooltip also shows the weapon damage added by combust attacks.

Using two claws, the attacks still expend the exerted charges, but do not trigger the support skills (fort/onslaught). The combust tooltip does not show the claw's damage, only global damage added via other gear.

I can't see anything on the tooltips which exclude claw attacks. For channeling attacks like cyclone, they do not use up the exert charges at all. So why are claw attacks using up the exert charges, but not doing weapon damage or triggering infernal cry supports?

Should claws do combust damage and trigger supports? Is this indicated anywhere in the tooltips?

Thanks!