Please update all plugins on the dev server and make sure it works fine BEFORE updating the production.
This is standard practice and should always be done for any updates, not just EE, but all plugins/themes.
So a single way to be sure if the plugin was updated correctly in to do it on the production? Am I right?
If you are asking if the only way to know if the plugin updated correctly is on the production site then the simple answer is yes, but thats the same for every dev/live setup. You can minimize the differences between the dev and live sites, use the same server on a subdomain for dev for example.