The article never claims it was "common for 18th and 19th century Chinese women to have two husbands". It says it was normal, but not common. It actually makes the point that it wasn't terribly.

As to how trustworthy the book is, Polyandry and Wife-Selling in Qing Dynasty China is based on original research of archival material. Sommer, is a legal historian who's looked at sex/gender studies in the Qing. He's fluent in reading and speaking Chinese and would not have had trouble working his way through the records. You can believe the book. Be cautious with the pop-journalism about the book.

The question isn't if it happened. It happened, but it wasn't common in the sense of "happening all the time all over the place". It was widespread but uncommon. The point of it being "normal" as the article claims isn't quite right, though. It was relatively rare and often these were short-term relationships, and it was rejected by the state and the elite. It may have been normalised among the communities where it happened, but not in the sense of normal for the Empire. We can't say exactly how many people took up the practice. Sommer justifiably makes the point that it surely happened more than what he's found records of, but we can't know to what extent since the records he's uncovered are so far the only records to be uncovered and publicised.

Did it happen? Yep. It the book accurate? Yep. Was it the usual practice for the majority of people? Nope.

For those interested, Sommer gave a talk about his research that's on YouTube here

edit: typos