ActionTiles definitely lets you change the order of your Tiles and Tilesets! I apologize, though, if this function isn't obvious. It is available in the Panel Builder (the same place you add, remove, and configure settings of Tilesets and Tiles)
Please be sure to read the "Cue Cards" throughout the App. The Cue Card for Panel Builder, says...
Once you enter Arrange Mode you will see the Cue Card for Arrange Mode.
Thank-you for enjoying exploring ActionTiles!
Customer support service by UserEcho