Yes, most R8 spindles have something like a dog point set screw that protrudes into the bore. The the arbor has slot that engages over the set screw. Supposedly it is there to prevent the tool from rotating as you are threading the drawbar. It is not really a key like a shaft key. R8 clamping force/ seating comes from the mating tapered surfaces. Some people remove the screw altogether, I suspect most leave it in. They can unscrew & drift in over time & that can be problem so be aware of that.
I don't think you have this issue as your runout problem, but something to be aware of on this topic. Some of the offshore manufacturers are sloppy when it comes to their slot dimensions. Sometimes too skinny or shallow or both. The set screw can then drag, even hang up & get stuck. That is a real headache & why some people despise them. So whenever you get a new R8 tool, don't assume its good. Gently push it up all the way finger pressure. If no scraping friction & taper seat engages fine, you are good to go. Test#2 check the drawbar threads by hand tightening too. It wouldnt be the first time they did a bad threading job or sent a mislabelled different thread.
I don't think you have this issue as your runout problem, but something to be aware of on this topic. Some of the offshore manufacturers are sloppy when it comes to their slot dimensions. Sometimes too skinny or shallow or both. The set screw can then drag, even hang up & get stuck. That is a real headache & why some people despise them. So whenever you get a new R8 tool, don't assume its good. Gently push it up all the way finger pressure. If no scraping friction & taper seat engages fine, you are good to go. Test#2 check the drawbar threads by hand tightening too. It wouldnt be the first time they did a bad threading job or sent a mislabelled different thread.