It being open source doesn't guarantee what you see on GitHub is the code that the extension uses.
I'm not saying this author is acting maliciously but a very common attack is to say something is open source, point to the repo but in reality the code running in the extension is unrelated to that repo.
This often happens with packages installed by popular package managers. The home page of the package will be linked to GitHub so it appears to be open source but the package itself has different code because most of these package hosting sites don't pull in code directly from GitHub. The package author can publish code from a private closed source copy of the code sitting on their dev box and no one would ever know unless they looked at the source code after installing the package.
Now, when it comes to Chrome extensions I do believe there's ways to check out the source code of any extension you use, so you could double check it there but then you have to worry about the extension getting updated too.