Half right. I can talk from kbin->kbin/lemmy. Since that is what I'm doing here.
Yep, when you search for a remote community your instance will connect to the remote one to look for that community/group/user. If it finds it, it will show all the info about it. Kbin will also automatically subscribe you to it.
Once the remote instance has your subscription, from that moment on it will send all interactions with that community to your instance. This results in some confusing things happening. You'll see a lot of new stuff start to appear, but sometimes old stuff, but not all old stuff. The reason for this is, if someone on another instance comments or likes a comment on old content, your local instance will not be able to action that like (or at least show it) or comment without getting the comments above that one up to the post. Which is why you'll see a mix of old and new content, but never all of it.