A lady at the deli that I used to go to all the time burnt herself with hot coffee. She smeared mustard on it and let it dry. No blistering.
I’ve never heard of putting mustard on a burn, but it’s quite effective taken by mouth for leg cramps, we kept packets of yellow mustard in the first aid kit when I ran track and cross country for this purpose. No idea why it works and it tastes disgusting, squirting the entire contents of a packet of yellow mustard into your mouth and swallowing, but it worked, again and again.