Each mail message "belongs" to the individual accounts. The "All" option just lets you see "all" (from multiple accounts) in one list of mail. There is no "dumping all incoming mail into All." There's actually NO mail in "All." It only looks like that.
A particular message can display in "All" and in the inbox of the account to which it belongs at the same time. However, that's just one copy of a message, not two. It's actually in the in the inbox associated with the email account.
"All" is a convenience feature so that you don't have to click through 3 inboxes to see all new email to you. It is not truly its own inbox with copies of the same messages. Imagine if you had 20 or 50 email addresses set up. To see all new email, you'd have to click through 20 or 50 inboxes. "All" (appears to) bring "all" inbox email together in one spot.
Same with All Trash and All Junk, etc. None of those are their own boxes with their own copies of mail... just a summary in one place of the various junk & trash, etc boxes associated with each distinct mailbox.
When you "take care" of email in All, you are actually taking care of it in the inbox or trash associated with the individual account. For example, if you delete a message from All it will be deleted from the inbox of the individual account. If you go into the individual inbox and delete a message from there, it will also be deleted from appearing in All. If you reply via clicking it in All, you are actually replying to it in the inbox associated with the individual account... the same as if you went into the individual inbox for a specific address and replied to it there.