Smart mailbox slow

I have set up a few smart mailboxes in Mail on my Mac, including 'Received today'. These are its settings:

Message is in mailbox: inbox — Date received: is today — Any recipient: contains: xxx.yyy — From: does not contain: xxx.yyy

where xxx.yyy is the part of my email address before '@'. (The reason for the last two criteria is that my wife also uses my computer for her emailing, and we have set her gmail account up on my computer in addition to my own gmail, icloud and btinternet accounts.)

When I turn Mail on, it takes around 10 - 20 seconds for all mail to appear in the main inbox; but it takes anything up to 2 or 3 minutes before mail appears in the smart (or not so smart) 'Received today' box. I should be grateful for suggestions for why this is so, and, if possible, what I can do about it.