I see it as a to/cc thing. e tags set up the reply chain but p is used for putting it in their inbox/notifications.
By default I just "reply all" by gathering all p refs in the note you're replying to, but this should be customizable
Discussion
Is this written down anywhere? (other than here ;-)
No but I think a e/p tag reply best practices doc/nip would be really useful.
More specifically: the pubkey you're replying to is the To: and the p tags in the note you're replying to is Cc:
Then you need to remember to filter yourself out of the Cc's unless you want that for some reason.