You need to use the state param to do what you’re after. That param lets you pass an arbitrary string which is then returned to you when they are redirected to your EBS.
So the link in your config to EVE Onlines OAuth page could include the users Twitch ID, or some other value your EBS knows to associate with a specific user, as the state param, so when the user clicks that and is returned from EVE Onlines site to your EBS you can check the state and know exactly who they are.