Sadly I am coming to expect that kind of incompetence more and more with chiros. Many PTs, docs, and chiros actually have no clue about strength training, yet because they have a credential their advice is supposed to be from an authority. You would think that someone who specializes in spinal care would have more knowledge as to how to strengthen the back though. Did they even demonstrate how those exercises should be done? If you just go out and "do the machine" without proper training you could completely f*ck your back up.
I'm not saying it IS your hammies, only that it MAY be. As for how it would affect your back, keep in mind that your whole body is an elaborate series of kinetic chains. Your posterior chain runs from the tips of your toes all the way up your back side and over your head to your eyebrows. If one aspect of that chain is not correctly performing its job, it will make another area pick up the slack, and eventually result in an overuse injury.
You have not earned the right to run yet. You have some strengthening to do before you shoe up and hit the treadmill. Your problem may well even be in your feet, but a simple orthotic or arch support is just a band-aid. There are exercises you can do for your feet, like towel-drags, that can help you strengthen your arches.
Keep in mind that I can't really recommend any of this specifically without actually seeing you. I really suggest a motion dna gait analysis so you can find out specifically what to do. Anything short of that is just guessing.
