When I read a message on my iPhone it seems to be by passing the Mailbox Rules when that message gets into my iMac. So I end up having messages in my Inbox instead of in the appropriate Mail folder. Why?
The mailbox rules on the iMac are only executed when Mail runs on the Mac. Thus to see the effect of the rule on the iPhone you have to have loaded the email on the Mac first.
To get the rules to work for all clients you need to implement then on the server. For most servers this means using the web version of the mail and logging on to the server there and then implementing the rules there. These rules will be acted on when the server receives the email and thus before either the Mac or iPhone has a chance to look at the email.