What should I expect if a company wants to file patent paperwork on my product?

It is unclear to me whether you have an application pending or not. Ideally, you will want to have some patent application filed before releasing information to them. Otherwise, you will want to have an attorney review the contract they are offering you. If they are offering to take over prosecution, you will want to make sure that deadlines are not missed and that competent U.S. patent counsel is hired. You will also want to file a Chinese patent application or PCT application within one year of the filing date of the U.S. patent application. If your product has a name, you should consider filing trademark applications in the U.S. and China. Who will own the patent? Who will be responsible for enforcement of the patent if there is infringement? Can you step in and enforce the patent if they fail to do so? Can you have your attorney review responses to office actions (to make sure they aren't limiting claims too much)? Can you file your own continuation application to try to get broader claims? Can you have your accountant periodically inspect the books and royalty calculation? Do they have assets in the U.S. (e.g., if you have to sue them for breach of contract or for dropping the ball with your patent application). Who has the right to sell in other countries? Can you file in foreign countries if they do not? There are many questions that need to be considered. I recommend that you sit down with a licensing attorney who is also a patent attorney, and discuss the details of your situation. I'm not sure that there is not enough information here to give you good advice.