I'm only replying because I think I use a slightly different technique. You can purchase hypodermic needles in a number of different diameters (also lengths, but that's not too relevant). I flatten the ends of the needles with a small file. You can also purchase flat end hypo needles but they are harder to find, etc. I roll out putty fairly thin - you won't need much putty to make numerous buttons. Then I use the correct size needle, punch the putty, push the button out using a suitable size wire and affix to the figure. I attach the end not touched by the wire when pushing it out of the hypo needle. Clear enough?
I didn't buy my needles from Amazon, but they have them. Look under Industrial & Scientific "hypodermic needle".
I've also used a punch and die set and roughly used the same process to make buttons, but not as often and normally I find this doesn't produce buttons of uniformity in size, shape.
All the best,
Dan