When someone posts something on a server he joined, the post doesn’t appear directly on the community from another instance. Why is that?
It sounds like you are referring the federation. When something is posted to one server, that server has to then propagate it to the other servers. That process is not instant; especially in large servers. In fact, right now with the Lemmy software it is a bit of a bottleneck that will be worked on soon. issue/3230
Another possible reason for this is caching. Browsers and servers save pages a lot to reduce load and make things go faster. That means that I sometimes you can see an old version of a page for a bit until it refreshes. Set correctly, a cache shouldn’t get too stale, and using the browser refresh button could fix it.
I think you used the correct word: fetching. The other instance has to go through everything new coming from the first instance and sync itself up. That takes time. How long? Depends on the machine and the load.
Also, if the comment does not appear at all the two instances might not be federated. That’s a whole different issue.