If you look at a manual rivet setter you'll get an idea about what the dies need to look like. The big deal with these is the small finger that sticks up. In the past, we've had to replace dies because someone lost control of a hex-height board and the weight of it was enough to snap that finger off the lower die.
From the comparison of what you've got vs what I've got, it looks like your rivet is installed the other way up. I've got the pre-formed side down, against the table. The "set" has a short alignment pin, and a curve that matches the shape I'd like to flare the cylinder end into.
One issue that I ran into is that the rivets probably should be longer than the vintage rivets that I have. Both the handles that I bought off Mouser and the modern PCBs are thicker than the vintage handles and PCBs, so there's not as much "flare" to hold the rivet in place. I'm not sure it is critical, though, because most of the insrtion/removal force is in the "Y" direction, with some in the "X" direction, but almost none in the "Z" (pull the rivet from the board/handle) direction.
Another issue is that the new boards need tweaking as to the placement of the holes. Some holes are too far from the board edge, and some have the spacing between the rivets rounded to the sixteenth, and so they don't line up perfectly with the holes in the plastic handles.
Vince