Yeah, the key thing here is that you (and OP) should be only using one account (in both of your cases, your kbin account) on the site your account belongs to (kbin.social). The site takes care of the federation. There's generally nothing you need to do † and you don't even actually need to know how the federation works. Simply treat the @domain thing as part of a magazine's name (eg, it's never just "memes" but "[email protected]").
† The exception is when you're the first person on your instance to subscribe to a sub on another instance. Right now this has a phenomenally bad UX and I'm hoping it will be improved quickly.