Hello,
Tyreman, joinery grade redwood is never going to be dry enough to make things like this from when first bought. You must prepare everything slightly oversize and over thickness, sticker everything in an indoor environment (not the shed!) and leave until there is no trace of movement. It might take a month for joinery stuff, it is not seasoned as well as furniture grade stuff. Reduce to final dimensions and then make your box. It might sound like a faff, but this is what high quality makers always do, there is no other way to be sure problems don't happen. If you don't, it is a lottery otherwise. And to be honest, an unrestrained solid top like this should always be made from quarter sawn stuff. It is hard to find quartered stock in batches of joinery grade redwood, but cupping will always happen with flatsawn stock to some degree. The degree of cupping is in effect doubled as well, when hinged on one side; all the movement appears at the front. Your work is worth the extra effort, I'm sure you'll agree; there is nothing worse than spending time on a job, to have something as simple as a board cupping, to upset you. But don't think these things are beyond control; they aren't, but you need to do what is necessary. Incidentally, that box might just be narrow enough to fix a solid bottom on, but that should be quartered too, and bone dry. Otherwise it might start to crack when it shrinks a bit. Definitely don't go wider for solid bottoms, either.
Mike.
