It's basically a pseudo-science. If they do any good then it's not because they are acting as chiropractors; they are doing the kind of exercise that a good physio would do; if they are following chiropractic theory then they won't do any good and could actively do harm.
The theory behind it is completely batshit.
As the legend goes, chiropractic medicine was born on September 18, 1895, when Daniel David Palmer, a magnetic healer in Davenport, Iowa, met a deaf janitor named Harvey Lillard. Palmer claimed they had a conversation about how Lillard’s hearing could be repaired by adjusting his spine, and with a crack of the back, the janitor’s auditory woes were cured. This was the launching point for the pseudoscience of chiropractic (how the practice of chiropractic medicine is commonly referred to). From there, Palmer continued to work on his theories, eventually opening up chiropractic schools that still exist to this day (yearly tuition at the Palmer College of Chiropractic in Iowa: $34,000. Acceptance rate: 100 percent), and the field of chiropractic medicine emerged. It’s possible that Lillard never consented to the procedure Palmer performed on him; some re-tellings speculate that Lillard was not fully deaf. But it’s more likely that, because there are no nerves in the back that can actually affect hearing, Lillard’s condition was not fixed with a back adjustment.
Palmer held séances to contact a dead physician named Jim Atkinson, and said that those séances helped him develop chiropractic. As he wrote in his 1914 book The Chiropractor:
"The knowledge and philosophy given me by Dr. Jim Atkinson, an intelligent spiritual being, together with explanations of phenomena, principles resolved from causes, effects, powers, laws and utility, appealed to my reason. The method by which I obtained an explanation of certain physical phenomena, from an intelligence in the spiritual world, is known in biblical language as inspiration. In a great measure The Chiropractor's Adjuster was written under such spiritual promptings."
It's rubbish because it's not backed up by good science. Worse than that, it's actually dangerous. There's evidence that it's responsible for some severe injuries and even deaths. Science Based Medicine has examples
When I listened to the Behind the Bastards podcast episode, they played a clip from a video of a baby being manipulated. It was upsetting just listening to it, without having the visuals.
I wouldn't touch it with a bargepole. Much better to go to a proper physiotherapist and to strengthen your back with pilates. Yoga could help as well.