First, make sure you are actually tightening the chuck to the spindle by turning the cams. They should gradually get tighter as you turn them. Tighten each one a bit at a time until they are all tight. You do not want to force them, but they do need to be tight.
After the chuck is installed, if there is any light showing at the front spindle face, then the fit between spindle taper and back plate is not correct, the tapered opening in the back plate that the spindle taper seats against is not machined enough. Like I said in my first post, WARNING! Do not take off too much material. Fit the parts together and tighten the cams down after rubbing a very thin coat of high spot blue (Prussian blue) on the spindle taper. Then take it apart and inspect carefully for where there is contact against the taper. Get some 220 grit sandpaper and lightly sand the spots that were making contact -- only the areas where contact was made. Don't sand on the spindle, or get grit on the spindle. Try to keep the angle you are sanding the same as the spindle taper angle. Clean everything up quite well so there is no grit and nothing interfering with the fit. Try the fit again with the blueing, and check the fit at the spindle face. If there is still not complete contact, try again, and again, and again, little by little, until the cams just pull the back plate against the spindle face all the way around, no light showing. It should require very little metal removal. It should still require tapping the chuck to remove it after loosening the cams. Stop there, you are done.