I haven't had that problem with the Hornady collet puller very often but I used to have to fiddle a bit to get the puller set up properly. It must be set so that the brass does not enter the interior of the collet yet applies a good grip on the bullet. I have also found that for pistol bullets which have little to no bearing surface available, by carefully sanding the bottom of the collet off a tiny little bit at a time, which decreases the amount of the taper on it, and repeatedly testing the grip, I can get the cam lock to work much better. How did I figure this out. Well, I chipped my collet on some 44 Mag that I was pulling, as the brass was getting up inside the collet just at the crimp. That is when I sanded it down, about 1/32 of an inch, trying to save the collet since they are not exactly easy to find and if you do they are not cheap and I still had about 100 rounds to do. Once I got it sanded down to the point the chip was not an issue, I found it worked far better than when it was new. I did the same to the one I use on my .357 and it wasn't even chipped. Far better action and grip. Wouldn't do it for the collets used on rifle rounds as I don't think it is necessary.
A person barely ever uses the collet puller, but when you do, you want it to work properly.
Another trick is to give a round a whack in the kinetic puller to partially pull the bullet, then use the collet puller to do the final pull. I like being able to recover the components, especially the powder cleanly.