As a non-native English speaker, who never says "Xth century" in my language, phrases such as:
In the late 19th century, they invented a lot of cool stuff!
... always forces me to stop and think about what is being said. "Obviously", they mean the 1800s, but to my eyes and my brain, the first thought it that they mean the "late 1900s", AKA the 1990s. I have to really concentrate to make myself believe that they are talking about "one century prior to what makes sense".
Even when the context should make it more or less clear, just seeing that "9" in "19th century" brings my thoughts over to "the 1900s" rather than the "1800s".
Also, what if I don't know for sure that the author of the text is a native English speaker? Maybe that person has the same confusion as I, and he really does mean to say the "late 1900s"?
You can imagine how confused I used to be as a child to see "20th century entertainment" logos and whatnot in the beginning of popular culture TV shows... or when it changed to "21st century" when it had switched over to year 2000! For the longest time, I assumed that they just wanted to be "futuristic" and didn't even realize that "21st century" actually means "the 2000s"...
Is this a common confusion? Maybe even among native English speakers?