Rosewood and other similiar species is grown/harvested/machined and built into furniture in the tropics. Thus its not been climatized to the drier and cooler areas in the northern hemisphere. The results is shrinking or checking of this wood, and I would venture to say this is whats going on with your bedroom set. Most likely it will continue in other areas, if you run the AC or heat, with humidity levels below 45%.
You can use epoxy wood fillers that matches close to the color finish.

Here is a link that might be useful: wood fillers

I doubt it is true Rosewood, as it would most likely cost in the 10's of thousands of dollars. I would go back to the store you bought it, and ask for assistance.

I also own Chinese rosewood furniture and have been searching for answers on refinishing and repairing some of my 35 year old pieces that I bought in Hong Kong. I am so tired of people like sloyder on so many websites declaring it can't possibly be real solid rosewood. There are many species of rosewood, which originate from several different countries from Asia to South America. Please do your own research before making ignorant comments.

The very fact that it needs repair tells you it's not the high quality "real" rosewood of the 18th and1 9th century.
Hong Kong?? Right..."real" rosewood!
Don't knock those with more knowledge than you have because you don't like the message.
Brazilian rosewood is the real thing, East Indian or Asian rosewood quite different.

That doesn't mean they're not "real" rosewood. There are about 33 species of rosewood and four of which grow in China.
Rosewood has been used traditionally to make furniture because it has
been proven to withstand degradation against termites and cold or hot
weather for hundreds of years. I've been told mine is padauk, which is just as hard, red, rare and beautiful. The point is, the OP never said they had 18th or 19th century furniture, so why would you want to even question the quality or the species?

And Philippine mahogany is real mahogany. ??
The point of question the authenticity and the type of wood is that an Asian "rosewood" is likely not properly dried, less dense and requires different handling than a real, dense Brazilian rosewood would.

I know this response is late, very late, but I couldn't help myself. People who comment negatively about rosewood furniture they have not seen, should simply be ignored. Responding to them isn't worth the effort. Let them embarrass themselves.

My folks bought solid rosewood furniture from an importer friend, in the 50's 60's & 70's. It is Thai rosewood that was then manufactured into furniture in Hong Kong (only the best comes from Hong Kong vs Mainland China) and exported to the US. It is extraordinary wood. Now, beginning in the late 70's, rosewood was being exploited so quickly that the forests couldn't restore themselves (it is now extinct:-). As a result, they started using greener wood. This resulted in the furniture cracking and shrinking.

NEVER NEVER NEVER use wood filler on rosewood. That would be a crime. Begin by oiling the wood with Danish Watco Walnut finish oil and apply with 0000 steel wool. If you do that every 2 weeks for about 2 m. onths, it should slow down or stop any cracking or shrinking. Then, have a professional restorer/woodworker/artisan repair the cracks. PLEASE don't start trying to make repairs yourself. You'll simply damage the furniture. Oiling once every year to 2 years will keep your rosewood in beautiful condition. Later on, you can oil less often. We oiled our rosewood every 5 years or so. It depends on your climate.

Lastly, congratulations on your high quality, gorgeous furniture. There is nothing like rosewood. Most beautiful wood on the planet.

Good luck!

I have several pieces of rosewood furniture that i need appraised and im out of the sf bay area. I am looking for someone to help me appraise the furniture which is over 40 yrs old. Can anyone point me in any direction?

I went through this and discovered, it's worth what someone will pay. I sold most of mine in 2016. It was from Thailand, made in the late 50's to late 60's. We are the reason Thai rosewood is extinct. They deforested their rosewood forests to extinction. I will never buy unsustainably sourced furniture again. I arrived at my prices using the original prices paid vs researching what it sold for on auction sites. This is exactly what an appraiser will do, while charging you about $200-$300 to appraise each piece, if you're lucky. Grain matters. Style matters. Age and origin both matter.