I spoke to a rep at the Mint yesterday about an order I wanted to cancel (the cancel button was not on the website for me to use). I explained the situation and she was shocked to hear about the Mint possibly charging these as a cash advance and said that would kill the program since no one would purchase the coins that way.
She verified the info with a supervisor and was told that the Mint will charge the transactions as a regular purchase. It is up to the individual credit card company to change the charge from a purchase to a cash advance or decide not to give miles for the purchase. The Mint will continue business as usual.
Keep in mind this was one rep and a supervisor that gave me the info and until an order actually goes through we will not know for sure.