The extension is not in developer mode, we are on the official Chrome Web Store and go through their (long) security reviews every time we release new versions.
The thing is that whenever a new version is approved by Google, it might take a few hours until it automatically being deployed to all our users.
Now, since our versions include multi-part deployments (Chrome Extension, our servers, our AppExchange package) and involve many API dependencies - once a new version is released, we ask users to manually update their extension version as well to align with everything else.
We almost always release the versions during the night-time (LATAM) to enable automated deployment to be completed seamlessly and then the users don't need to do anything.
In other cases, the users need to follow the mentioned instructions in order to manually update the version.
These steps are taken from Google's documentation, and although it's called "Developer Mode" it's not related to the mode of the extension itself.