It’s important to understand what causes the warp or twist, and for the most part, its uneven moister absorption or drying. If you purchase thin boards, it is important to provide equal air movement around the board. If it is just a few boards, then just lean them against a wall or work bench to allow equal air movement. Do not lay them flat on any surface. This does not allow for equal air movement. The same applies if you resaw or plane your boards. You must provide for equal air circulation around the board. If it is a lot of boards, it is best to stack and sticker the boards. That is stacking the boards on top of each other with stickers or thin sticks in between each board to allow for equal air circulation around each board. Either way, you must allow for some time to allow the boards to equalize to the environment of your shop.
As for trying to take the cup out of a warped board, you might spray a little water on the cupped side of the board, then apply a little heat with a heat gun or hair dryer to the wetted surface. This trick works sometimes.
I make and sell a lot of ornaments each year, so I stack cut all of my ornaments. Beacuse I have a full woodworking shop, I can mill all of my thin stock. I either plane or resaw my blanks to 3/16” thickness. I will usually stack three layers. If any of the boards have a cup in them, I’ll stack the cups against each other, then clamp the stacks together along the length of the boards. This will flatten the stack. Then I apply hot glue along all edges of the stack. After the hot glue sets and removing the clamps, the stack will be reasonably flat enough to cut.
These picture show a stack of boards I bought online before I got my band saw for resawing. I cut the stickers from 3/4” pine.