As Tiase rightfuly pointed out.
They conspired and comitted treason, Jon being resurected or not they were going to hang because edd and the Wildlings have control of Castle Black.
Now Jon is alive, therefore it's normal that he carries out the sentence of those who betrayed him.
Olly is yes a child of war, doesn't have the moral aptitude to understand Jon's choice, but he still murdered him. Jon can't let someone that murdered him and betrayed him just live on like nothing happened.
As Tiase also said, it's normal to try and seek revenge on those who wronged you. And in this case we are talking about people that killed you, ended your life. Nothing unusual to try and take revenge.
So add Revenge + Moral justice = Nothing out of the norm here. Anyone in his place would do it. People that say otherwise are liars.
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Now that he saw death (and oblivion) his character will change.