How to force the Outlook rule to be server-side?

Does your MS-Exchange server provide web-based access to your eMail? If so, try logging into that and creating the rule there (and then it will have to be server-side).

If you have the destination folder in Personal Folders, it would be in your pst file(located in PC) and the rule will become client-only. But if you place the destination folder in inbox, the folder will be in your Exchange and the server will process your rules.

Being marked as "read" is a client side action not a server action. When you opened the message on your phone it (the client) read it and then told the server to mark it as read.