Veyran + Aria of Flame

I got a question regarding an interaction and I would be super happy if you cound help me out here.

When Veyran, Voice of Duality and Aria of Flames is on the field and I cast an Instant or Sorcery how does the interaction work? I assume Aria of Flames would get a verse counter deal 1 then it gets another verse counter and deal 2.

So the next Instant or Sorcery would add 3+4 counter dealing 7 dmg for the second spell casted

Spell 3 would deal 5+6=11 dmg

etc.

Is that correct?