IIRC, if a representative posts on one instance and a constituent replies on another, the original poster is unlikely to see the reply. Not a good way to communicate with constituents.
This is not how Mastodon works, the point is exactly that cross-instance communication can work smoothly, and it does. Replies show up on your notifications just like any other similar platform, whether they come from your instance or another.
I haven't used Mastodon much, but I have seen replies that weren't visible. There was a big thread with several generations, some visible to the original poster (who showed me this), some not.
Guessing… server blocking? Grandparent replies (the thread was big)?