Regardless of the quality of a box, if you do too much too fast, you could shock the wood into some kind of warp. A little at a time, without trying to test the outer limits is good. Wiping down your cedar liner with a damp (not dripping wet) cloth will allow some expansion in the wood. If you find the rh still too low, do it again; let the wood take on the water at a rate that will not alter its shape.
That being said, a cheap box that warps easily was prob going to lose its seal pretty quick anyway.
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