I often here a big deal made out of how Constantine tricked the Presence. I have read the scene in question and I don't see what a big deal it is. How did John trick him?
How do you trick a being like that? If this is similar or the same Presence from Lucifer you cannot. At the dawn of time it would know every possible trick Constantine could do and every way to counter. It would know how to set up events to have every possible counter. Heck, it would precisely know what trick he would try. It would have the power to rewrite the rules of reality to whatever it wanted to counter anything John could do. All the legions of hell would be nothing to the Presence. So why would it be intimidated from John's threats?
Isn't it a bit more likely that it helped John because it may actually like what he is doing? Generally fighting evil and help keeping heaven and hell in line.