I'll go back and re-read the link you sent to see if you already put details there.
More about making and setting rivets is at
Brooks saddles - modifying the frame/recovering
I anneal after the hammering to size and shape using the anvil, and before the final shaping work using the vice mounted drill.
I place the rivets onto a heatproof sheet and then heat the copper to cherry red with a MAAP gas torch then quench in water.