The "alpha roll" suggests that it imitates how an alpha wolf will discipline a subordinate pack member by forcing a dog on his side and pinning him down. The dog trainer technique is to grab the dog by the scruff, throw him down on his side or back, and growl "No!" in his face so that you can assert your "leadership" over the dog.
This is extremely outdated and dangerous information. Being your dog's leader is not about who's boss, using punishment or “alpha rolls”, or forcing your will upon your dog, it is about the relationship you have with your dog.
Grabbing your dog, shaking him by the scruff, forcing him to the ground, and growling at him is aggression. Regardless if done by a human or another dog, it is being a bully. When you do this, expect a fight that you will not win. If you are able to do this without getting bit, it can certainly stop a dog from misbehaving, at least momentarily. However, it teaches your dog to resent you and can come out later as aggression, or be directed inward and express itself as fearful behaviors or a general lack of interest in life.
If your dog is doing something where a correction is needed, the correction should be quick, calm & quiet, and over in an instant. It should send the simple message "stop doing do that", interrupting the unwanted behavior, allowing you to then redirect the dog to a better behavior. Similarly, dogs will give a quick nip to stop an unwanted behavior and then go back to socializing. Physically trying to roll dogs into a submissive position onto their back is not quick, it is drawn out, dramatic and will put most dogs into a panic self-preservation fight mode where you are asking to get bit. This is a great way to undermine your relationship with your dog.
Being "rolled" is done BY a dog, not TO a dog. A dog will roll over on his own out of respect and in response to calm-assertive body language, or out of trust during play, not because he was forced. If your dog rolls over in response to your calm leadership, without you ever touching your dog, that is a true "alpha roll". Do not confuse this with your dog being able to tolerate handling. Asking your dog to roll over so you can examine his belly or feet is done in cooperation and offered out of trust and respect.
So what should you do instead to get real, lasting behavioral changes in your dog? Work on your relationship with your dog. Discipline instead of punish, encourage instead of discourage. Go for walks, have fun, play searching games. A dog who routinely plays tug, fetch, and chase me is far more likely to respond properly than a dog that is constantly punished by a bully.