It's real. Most of their powers deal with probability alteration, I guess it could be considered some kind of unconscious reality warping.
I know that Longshot, for a while, had to have pure motives for his luck to work. Later on they kinda retconned that and revealed that it was a balance thing, the more luck he used for himself the grater the chances that he would cause catastrophic bad luck somewhere else. He also has psychometry, but most writers seem to forget that.
Domino says that her power allows her to "have things go her way" as in the dominoes fall the way it's most convenient for her. I've never seen her actively "wish" for the outcome she wants like Longshot, but rather that whatever happens is favorable for her. Apparently she has to see the attack or whatever coming, she has been caught unawares if her attacker uses misdirection to conceal the real purpose of his/her attack.
Roulette had luck powers in the beginning instead of the Tarot cards she used later. She made black "bad luck" discs and white "good luck" discs. When she dropped or threw them and the impacted a surface the corresponding luck would create an effect. She had some control of the outcome since she actually turned off Speedball's powers once and then reactivated them at an intense level that he couldn't control himself. The discs can be used against her.
I'm not much of a Spidey fan but I know Black Cat started by faking her bad luck powers and then went through a process that actually gave her her bad luck powers.
