How can I make sure that the extensions I use are open source and they
use the code that they claim to be?
Short answer: you can't.
Long answer: To check if the source code and the binary belong together, reproducible builds (see https://reproducible-builds.org/) would be necessary. Usually, everyone who compiles the source code will get another result.
If you want to make sure that your binary belongs to the source code, however, you can compile it yourself, which is not an easy task though.
Does it mean that the app is not open source?
The Github page contains only one commit (https://github.com/adblockultimate/AdBlockUltimate-chrome/commits/master), so there are two possibilities:
- It is Open Source. Then it was a project somebody wrote two years ago, one year ago he/she uploaded it to the Chrome store.
- it is not Open Source.
If you want to find it out, you should write a mail to the developer or open an issue on Github.