It may help to spray the button die with a dry lube to help the vinyl move and prevent tearing while it is being formed over the shell. Air born silicone can cause health risks and problems with fish eyes in paint.
I Use the same button press for all leather, vinyl, or any fabric. If the leather is to thick for the button counterpart you have to skive it down. The same trick works for the vinyl. You can skive off the fabric on the back of the vinyl. Its a little bit tricky to find out the right adjustment if you you use a skiving machine.
My problem was that the counterpart cut off the vinyl if its to thick. So I skived down the backing cloth and the little foam part some vinlys have. The Problem of the backing cloth (often Nylon) is that it blut down the skiving maschine fast. Meanwhile i have 2nd skiving maschine so I use my old one only for the vinyl jobs and the other for leather.
Sorry I dont have any advices. I think our button maschine was mounted on the table long before I was born. And also the button pices will suffice till I quit work. :D
But I shot a picture today to show how the skived vinyl have to look that it works with the button maschine