I've got some arabesque terracotta tile on order from Ken Mason for a backsplash. I could use some insight on how to prep the walls. Should I use cement board, mud because I'm pretty sure the tiles can't go directly on the drywall. I've laid both ceramic and Saltillo tile.

The tile is about .5" thick

I've done ceramic tile backsplashes but this is a first for me so a little guidance is appreciated. Thanks in advance.