iOS new mail does not appear in inbox

I am using iOS mail with an IMAP push enabled inbox. Notifications for new emails appear instantly but sometimes the new email does not appear in the inbox (it seems that it needs to be downloaded first, taking up to 2-3 seconds). Is there a way to eliminate this time and always have the mail in the inbox without waiting for it to appear? This happens on multiple different accounts. Is this intended behavior and can it be tweaked?