Interesting questions. You've come in with language I"m not familiar with.

I would think volitional and non volitional are other perspectives on what I call traditional and non traditional. Traditional nuerofeedback is entrainment, in which the doctor assesses what kind of eeg activity would be an improvement for you.

THen a protocol that rewards that selected eeg activity is used and the selected eeg activity is rewarded Thus Entrainment., and I suppose volitional in that you have signed on to make these specific eeg changes. I use several entrainment techniques - z-score training, alpha theta, etc.
Non traditional, non volitional is a disentrainment system called LENS.

I use LENS also, often. Lens encourages the brain to focus upon itself and repair itself. To break bad habits, to take down the walls of inhibitory neurotransmitters that trauma puts in place and reallocate resources.
Both of these types of training technologies now have FDA approval. All of the protocols are research based. However most often this research is not large, funded, double blind.

There are many problems with conducting that type of research in the private clinic setting, which is where this work comes from. We see what works and then we can't not provide it (hence the problem with double blind). What most people think of as researched based, is from the pharmacological model, which has tremendous ethical problems. I do this work, because it works.

What claims are made for it? It works. Are you looking for something more specific here? Nothing works for everyone. I have seen my techniques work for people with depresssion, migraine, pain, anxiety, traumatic head injury, dissociative disorder, add, adhd, ocd, panic attack, and many other less clearly diagnosed complaints about life.

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I'll consider it, but am of course, hesitant.

I don't spend $ too often on medical, since I don't have insurance.