Whenever you cut wood, it exposes fresh surfaces that will dry if they’re too wet. Even a little bit of excess internal moisture can cause a lot of warping if the wood is thin, as yours is. A better approach is to allow about a week or two of drying time after every major sawing operation, then mill out any distortion that sets in during that period. Of course, this means starting with sufficient wood thickness for planing and jointing right from the start. You would have been very lucky indeed to cut wood as thin and wide as you did without encountering warping. I wish there was some trick I could tell you about to fix your warped tray by steaming, clamping or bending, but I’ve never seen such a thing work long-term. A better approach is to somehow modify your design so it includes additional wood strips along the bottom that would pull out the warp while also looking right.
What caused the new tea tray I made to warp? I glued thin strips of walnut, maple and purpleheart wood along the length of a piece of 3/4-inch thick oak, then sawed this wood in half and glued the pieces together along their edges. The finished tray looked terrific, but after a few weeks it warped and the whole tray is now twisted. What went wrong? How can I fix it?