I take a punch I have with a rounded end and set that in the opening of the rivet then give it a whack, that usually flares the outside edge of the rivet outward slightly. Then I work at expanding that with the rounded side of a small ball peen hammer. I have pretty good luck doing it like that, maybe one in four bends over and I have to cut it off and start over. This isn't something I tackle very often but I've done it a few times and this was the method I arrived at through trial and error.
I see it a lot in auction listings "Factory Rivets" unless you bought the cymbal new or it's a real hack job of drilling how would you know factory vs a pro job of drilling (either at a shop or just someone that knows what the heck they are doing) and does it matter that much? Mostly an...
I give examples of how Zildjian do it with some specific tool they have, and a non Zildjian one. I've also got examples of rivets where somebody pounded it on the end to spread it out but I didn't include those photos in the thread.
You can also hammer it on the edge to just squash the whole rivet out. I don't have a picture of that handy, but I'll add one if I come across one.
The method KO is describing is a bit more civilized.
Split rivets sound just as good as tube rivets. The only reason I don't use them is because of their propensity to grab ahold of cloth, thread, cables - anything that comes into their vicinity. Even the tube rivets I use will do the same if a smooth flare is not done.
I have used Bosphorus rivets before but never tried the Zildjian ones. These days two cymbals with rivet holes get a suitable sized screw from my tool box full of them. I screw them in when needed and unscrew them when not needed. Keep a couple in my cymbal bag's pocket. They work perfectly and never fall out when playing. But that didn't answer the question, I know .... sorry ....