A couple of things... along with builders query about the type of tiles, I would ask if the shed floor is made of waterproofed (treated wood There's a lot of difference between a shed floor that was mounted on something to keep it off the earth and one using that floor in direct contact with the ground.
If, however, you proceed you'd want to use at least 1/2" but more likely 5/8" treated plywood for the base for your tiles. You'd need to make sure everything is non-moveable since, if you're going to use grouted tiles you'll exprience cracking if the substructure isn't strong enough...