I assume that you are using an exchange server.
Some rules are client side rules and some are server side rules. Client side rules can only be run when the client is actually running on the workstation. Usually things that will make a rule become a client side rule would be if the rules uses a local PST folder as the storage location of the email, or if the contact is an Outlook contact not an Exchange contact.
If you are not using Exchange then all rules are processed as client rules.