Medic Archetype clarification

[Gamesman02]

I Looked but didn't see this, apologies if I missed it.

Looking for clarification when Treat Deadly Wounds as a Medic archetype. Specifically the bonus at higher DCs.

When taking the Medic archetype:
You become an expert in Medicine. When you succeed with Battle Medicine or Treat Wounds, the target regains 5 additional HP at DC 20, 10 HP at DC 30, or 15 HP at DC 40.

As an Expert in the Medicine Skill:
If you’re an expert in Medicine, you can instead attempt a DC 20 check to increase the Hit Points regained by 10; ...

Does this mean that when attempting TDW at DC15 and roll is >19 that the patient receives 2d8+5, but if attempting a DC20 and roll is succesful, the patient would receive 2d8+15?

[The Raven Black]

DC 15 = 2d8 or 4d8 if >25 (critical)

DC 20 (if Expert or better) = 2d8+15 or 4d8+15 if >30 (critical)

Note : with Medic, you can use Assurance on Medicine and automatically get the DC15 normal (not critical) success result as soon as level 2.

[Deth Braedon]

for the Medic archetype, this portion of the dedication text:
When you succeed with Battle Medicine or Treat Wounds, the target regains 5 additional HP at DC 20, 10 HP at DC 30, or 15 HP at DC 40.

might be simplest to think of it as a modification to the CRB text, like so:

If you’re an expert in Medicine, you can instead attempt a DC 20 check to increase the Hit Points regained by 1015; if you’re a master of Medicine, you can instead attempt a DC 30 check to increase the Hit Points regained by 3040; and if you’re legendary, you can instead attempt a DC 40 check to increase the Hit Points regained by 5065.