It says it can activate on all default weapon attacks but it’s a bit ambiguous.
So the key word with skills like savagery is the part in the description that says "When used as your default weapon attack. Savagery and firestrike both have this description. Cadence has this description, but i don’t believe the third strike has a chance to proc them as it is its own “thing” so to speak. The first two strikes do, however.
Yes, Cadence 3-rd hit doesnt count as “default attack”.
So make good use of skills like Necrotic Edge, you should use Fire Strike or Savagery, or item-provided ability based on one of them).