Procession and Throne room interaction
The Procession rules state:


  If you Procession a Procession, you will play one Action twice, trash
  it, gain an Action card costing more, then play another Action twice,
  trash it, gain an Action card costing more, then trash the Procession
  and gain an Action costing more than it.


There is no reason to assume that Throne Rooming a Procession would behave any differently: they both allow you to "play an Action card from your hand twice".  

So your second scenario is correct: you would play two different action cards twice, not one action card four times over.