When you include the library as required in your composer file, Craft will automatically download the package and install it in the global
vendor directory rather than in your plugin directory (since both are inside the
You don't have to include it and you don't have to take care for certain other plugins that require the same one.
This process is done while running
composer install >>yourplugin<< or
composer update so everytime you make a Craft update it will search for new required libraries in your plugin but it won't do it during the installation of your plugin since every library should already exist - unless you add the dependency after your composer action ->
composer update will solve it