Hi Swerdk, Your spindle is properly marked. You need to put an index mark on your cams (as shown in the annotated photo by Jim). With the chuck off, you ought to be able to look in the pin holes of the spindle nose (perhaps reach in with your pinkie finger). You could even pull one of the cams out (remove that small cap screw, but becareful as there is a small spring and plunger at the bottom of the hole that the cap screw is in).
I understand that your chuck seems to mount up well. It sort of looks like the cams are not turning the correct amount (comparing your photograph with the one Jim provided) - either too much, or not enough - which means you may need to adjust the pins as described above. Those pins are what keep the chuck secure on the register (the tapered portion - as Bob identified). A properly secured spindle attachement (chuck, face plate) is critical to the safe and satisfactory operation of a lathe. I advise that you not operate the machine until you know the device is properly secured to the spindle.
The pins being right or wrong, will not change the runout (unless they are so bad that they do not pull the chuck on at all) - since it is the register that is locating the chuck. All the pins do is keep the chuck pulled in against the nose.