How do I stop hamstring tightness?
It would be a good idea to have the muscles balanced-not have quads significantly stronger than hammies. Incorporating yoga into your training would also help with keeping the muscles stretched. Also foam roll regularly. Stretching helps, but rolling is like a self massage. Actually getting a massage on occasion may help as well, as myofascial release (better than massage with longer lasting results).
You are probably on to something there with your quads. They oppose your hamstrings and so some hamstring problems are aggravated by a person not stretching their quads first before stretching their hamstrings. Do some reading on what is called slow static type stretching and also on dynamic stretching. Dynamic stretching is breaking down various muscle groups and isolating certain muscles and stretching them first before stretching others and then stretching muscle groups in a particular order for achieving better results and increasing your flexibility. You will in that what I am saying about the quads and how they keep tension on your hamstrings and why you should stretch your quads first. Also start running more backwards when you do some of your training and in your practices. You almost never hear of a basketball player or a defensive corner linebacker or safety in football having issues with their hamstrings for that reason. However running backs for instance are notorious for having problems like that because of always running and driving forward. After warming up stretch your quads first and then your lower hamstring followed by your middle hamstring and that followed by the upper hamstring and only then after stretching those, then stretch your entire hamstring muscle group collectively. Don't neglect your lower back also in all this to further relieve any tension on your upper hamstring after you have stretched your quads.