The issue you’re describing is humidity related. Puzzle boxes operate on tolerances measured in the thousandths of an inch and are particularly intolerant of extremes in humidity.
Unfortunately, there is no other way to make them; it’s simply not possible to make a puzzle that works in the dry heat of Arizona as well as the humidity of Singapore...or New Zealand for that matter. The wood expands and contracts according to the environment; quite quickly as you’ve found.
For that reason we advise our collectors to keep the puzzles in humidity-controlled environments, using dehumidifiers or air conditioning to maintain a proper amount.
We keep our shop between 40 and 50% humidity during production. I checked your location and found that ambient humidity is a whopping 90% there. Constantly fluctuating humidity is not good, and will likely cause warping over time; 90% humidity is already an extreme environment for puzzle boxes I’m afraid.
The wood will react the other direction if put in a dry place, but it will take longer to dry out than it took to absorb. If you don’t have air conditioning or a dehumidifier, my recommendation is to put the box in an airtight bag with some desiccant and a humidity meter to monitor it. It will take some time in the recommended environment to return to normal operations, but it will eventually happen. Don't leave it in too long and dry the wood out entirely!
If you’re intending to collect puzzle boxes I would very much recommend setting up a cabinet with some kind of humidity control system, as you will run into these issues with any boxes you obtain that are high quality with close tolerances. If you find a good storage solution (dehumidified containers or a cabinet), you should be ok to take them out and solve them, but I wouldn’t leave them laying out as the absorption can be rapid.