
Headcanon: Alastor was completely terrified of dying and going to Hell before making his deal.
While Alastor appeared to be practicing some form of Voodoo or Black magic while making a deal, I get the feeling though that he was some raised with a combination of Voodoo and Christian beliefs; and was either an atheist or cafeteria-christian as an adult, likely only going to church with his mother.
However, while living in the high life in New Orleans, something scared Alastor, or made him realize that his life is finite and that he will not live forever (this would've likely been triggered by the death of a loved one,Mimzy or his mother, or even staring long enough at the lifeless corpse of one of his victims). This causes him to panic:
"This person died today..."
"I could die some day..."
"I AM going to die someday*...!*"
"...And if Hell exists, that's where I'm going!!!!"
Keep in mind, at this point Alastor has no idea what Hell is like, let alone that it even exists, he more than likely imagined Hell as a fire and brimstone raining realm where he'd be wailing in agony in a lake of fire. Also Alastor does seem to live very vicariously while in New Orleans, even outside of his murders.
So with this knowledge, Alastor has two options: Repent and turn from his vicarious life-style, and potentially go back to living in lesser conditions(I get the feeling Alastor wasn't fond his way of life before New Orleans), OR accept that he is going to Hell, but he can try to secure a spot amongst the highest ranking demons by making a deal with one. I think we all know which one he picked.