I’ve never been able to successfully sync posts from a kbin Magazine to Lemmy. I also haven’t seen Lemmy users show up in kbin communities so I assumed that subscriptions were unilateral (kbin users have access to Lemmy but not vice versa).

Do posts from one website only appear on the other if the community already has subscribers?

Yes.

When instances federate, they don't just automatically share content. They only share the content from a specific community/magazine if somebody from the federated instance subscribes through that instance to the community/magazine on the host instance.

If I'm following it all correctly, what actually happens under the hood is that subscribing to a community/magazine on another instance triggers the creation of a new community/magazine on your home instance, which from then on will mirror the content on the original.

So in your example, the original is survey_polls@lemmy.world. Initially, it's not going to appear on kbin.social - there has to be interest in it first, as demonstrated by the fact that somebody from kbin.social subscribes to it.

At that point, for all intents and purposes a new magazine is actually created on kbin.social - survey_polls@lemmy.world@kbin.social. So you're not actually accessing survey_polls@lemmy.world through kbin.social - you're accessing a mirror that's hosted on kbin.social. And the trigger for creating that is someone on kbin.social subscribing to survey_polls@lemmy.world.

At least I'm pretty sure that's how it works - note that I'm just some guy who likes to figure out how things work and not a dev.