Question about Digi-Clone w/ Double Barrel in regards to Mayhem mode

Do Mayhem modifiers count the digi-clones damage as weapon damage or action skill damage? If I have the modifier that nerfs certain gun types and buffs others, will my clone be affected?
I feel like the game isn’t really providing a lot of information on those things which makes it rather though to figure out how Mayhem Modifiers affect him.

Yes and yes.

The gun that the clone shoots is affected by all modifiers.

Action skill damage would be Dopplebanger, which is also affected by other modifiers (normal attacks and bullets).