Unified Inbox for all, including fetched mails

Unified Inbox for all, including fetched mails

I fetch mails from different third-parties mailboxes. But I need to switch mailbox too see fetched mails. It's strange. All mailboxes have one shared disk space for own mail and fetched mail, but why do we need to switch mailbox (on the left bottom)  to connected mailbox every time.
Maybe I have't learned to use Zoho Mail yet?
And I want to see all the mail in WEB-UI, and also in third-parties Mail Client