Definitely sounds like the wood was not properly dry. I always like it when people share pictures, I would like to see some if that is not too much inconvenience.
About your problem... There are some things you can do to prevent wood losing it's moisture, including some oils that will not change the color of the wood, also can seal the whole thing with polyurethane, this is basically painting it with plastic, nothing gets out nothing gets in, effectively sealing the humidity inside, and making it waterproof on the process...
The other option is to fight it back, with some clamps and glue put the stuff back together until it stops doing it.
Now if you really want a good quality board, then probably will have to keep on shopping.
Like many others I have ordered boards and pieces from Chessbazaar. The pieces are fine but I find that on numerous boards that I have the squares start cracking. It is never the light squares (the boxwood) but rather the dark squares (the rosewood or ebony) that cracks. On the lovely ebony and boxwood board with the sheesham wood margin the squares have even started to separate!
Does anyone else have the same problem? I cannot believe I am the only one who suffers. The problem is obviously that the wood is not completely dry when they construct the boards - and so as it continues to dry on the board it starts to crack.