I'm not sure this is something you're going to fix, Eyvind. I'll be interested to see what people have to say. It may help to try a different clay body with less shrinkage/more grog/sand. I have a Peter Pugger and have considered using it from some extruding, but I'd build a tile press if I were going to make a lot of tiles.
Presently, I make tiles from slabs. They don't have to be perfectly flat as I only use them for coasters or for wall tiles. To keep them from warping, I dry them between sheets of plaster board (wall board/gypsum board/sheet rock). I wrap the edges of the plaster board with duct tape to keep it from crumbling into my clay. Of course, if your tiles are high relief, this won't work for you, but otherwise you might give it a try. You'll need a weight on top.