How can I move an email without deleting it from iCloud server?

I have local rules on my Mac to move emails from certain people into their own local folders, and sound a unique alert. The problem is that it appears that moving it causes it to be deleted from iCloud's IMAP server, and therefore not delivered to my iOS devices.

When I changed the rule to copy rather than move, I'm left (of course) with duplicate emails in the local Inbox folder.

I tried creating iCloud Mail folders and using iCloud Mail rules to move certain emails into those folders. The problem is that I can't sound the alert: it appears that Mac Mail rules only apply to mail coming directly into the Inbox. (Also, only iCloud Inbox items get 'pushed' -- the mail in my John folder can only be retrieved when Mac Mail polls every N minutes.)

I'm new to IMAP, so I may have missed the solution. Can anyone suggest how, using iCloud Mail, I can:

• See the same email in my Mac and all my iOS devices
• Automatically route certain email to special folders and sound an alert, at least on the Mac

Thanks-

Chap