Carefully wipe a very thin coat of high spot blue onto the empty face of your lathe spindle. It is of the HIGHEST importance to get this blue in an exceedingly THIN coat on the surfaces,or you will get readings no better that the thickness of the blue. Then,without tipping the chuck any more than you can,mount the chuck onto the spindle and tighten down the cams. NO NEED to get the blue into the cams!!
If all seems to mate up well,loosen those socket head cap screws that hold the front part of the collet chuck on. See if there is any room inside the mating parts of the chuck to slide the chuck's front part sideways If so,replace the screws,leaving them snug,but not tight. Then,put on a collet of KNOWN ACCURACY(collets can be bad too!) into the chuck. Hold an end mill shank (NOT DRILL ROD! it is not accurate enough) in the collet. indicate it and tap the collet sideways with a small plastic or brass hammer. Take your indicator probe OFF the end mill while you do this. You can ruin the indicator by shocking it with taps. Mess around until you get the end mill to run .0001". Then,CAREFULLY remove the chuck and progressively tighten the screws. This may throw it out some. You have to keep on till you get it right.
If the mating surfaces do not mate up well,remove the chuck and look where the blue has transferred to the mating surfaces on the chuck. This will tell you if the chuck's tapered hole is too small or too large,and if the other surface is not going down flush.
If the tapered hole in your chuck is too small,you probably ought to just send it back. Otherwise,you must put it back side out in a 4 jaw chuck and with a good dial indicator,carefully get all the surfaces to run dead nuts true. Then,you must take a GOOD tool post grinder and grind a bit out of the hole. You can go by degrees. Undo the cam pins on the back of the 4 jaw chuck AFTER marking one pin and which hole it went into. Without bumping the chucks,and with blue on the spindle again, press the back of the collet chuck against the spindle. You don't need to install the pins to do this. Check where the blue touched,and find out if you need to take another slight grind off the back of the collet chuck. This is the simplest way I can figure to get your chuck to properly match your spindle.b If you don't get the collet chuck to run true on all surfaces before you grind anything,you will likely screw it up for good.
If you do a good job of fitting the chuck to the spindle and it still runs out of true,the hole and taper where the collet goes may be ground off center. You really should try loosening the cap screws first and see if the chuck can be adjusted sideways.
I always do this exercise when I get a new chuck,to get it to run as true as it possibly can.
When I got my new 16" Grizzly,I kissed the surfaces of the spindle with a tool post grinder,including the tapered hole. There was a bit of runout on the surfaces. Not a lot,but I'm a perfectionist. I don't advise anyone to try doing this unless they really know what they are doing. You can't take metal off once it is removed.
Once the surface had been ground,I put on each chuck and faceplate with blue,to make sure everything mated up perfectly.
If you got the chuck cheap,or if you like to overcome problems,time no object,you can keep it and try to get the problems worked out.
Not to confuse you,but here is a list of things I can think of that COULD be wrong with the collet chuck:
1. Problem with the chuck not mating up to the spindle nose
2.The front of the chuck may just need to be adjusted sideways. I have a Cushman collet chuck that takes much larger type collets that I need to adjust. A Cushman was an excellent chuck,so I'm sure it just needs adjusting.
3. The hole and/or the tapered hole that holds the collets may be out of true. The straight part of the hole could be too large. The hole could be ground at a slight angle to the centerline of the chuck. The tapered part could also be ground askew.
4. The back side of the chuck could have been ground at a slight angle to the centerline of the chuck. The tapered hole could also be ground askew.
These imperfections need only be slight so that you cannot detect them by eye,and they must be determined by indicating everything in a methodical manner.