When to roll initiative? Options

[Tseims]

My group is on a run and we get into a shootout. My character knows that the enemy has vital information that my character needs, so he tells everyone to leave the leader of the goons alive.

After the shootout my character goes to the surviving enemy and begins interrogating him to try and get the information out of him. Suddenly another player decides that his character tries to shoot the man dead during the interrogation.

Now, would his character get to shoot the enemy before I get to do anything? Or should we roll initiative to find out if the other player's character can shoot the man before my character can do anything about it? How about a surprise test?