Oh - for that you need to make sure that you’re connecting with the right Access Token & Secret. ie: Consumer Key & secret are from your app, and the Access Token & Secret is specific to a user who authorized your application.
Unfortunately to do this for many users - you need Sitestreams https://dev.twitter.com/streaming/sitestreams which are closed at the moment. (userstreams are designed for 1 user only, so running multiple streams for multiple users won’t work)