Hi,
I find an similar thread about your question, please refer to:
https://social.technet.microsoft.com/Forums/office/en-US/4f4e3a18-1707-4135-8f8b-b15775cbb7ac/everytime-i-start-outlook-2013-my-rules-in-owa-get-reordered-rules-that-only-appear-in-owa-move?forum=exchangesvrclients
"By default, if Outlook is configured to connect to a Microsoft Exchange Server computer, message rules that you create in Outlook are applied to your e-mail messages even if Outlook is not running. These
message rules are server-side rules. If a message rule specifies an action that cannot be applied on the Exchange Server computer, the rule is a client-only rule. An example of a client-only rule is a rule that moves a message to a particular folder
in a personal folders file (.pst). A client-only rule is only applied when Outlook is running. When you use the Rules Wizard to create message rules in Outlook, you receive the following message if you create a client-only message rule: This rule is
a client-only rule, and will process only when Outlook is running."
As Ed mentioned "some rules run server-side, some run only on the client", if you get this warning and you want to delete those problematic rule, we can run Outlook with the /cleanserverrules switch to delete server-based rules.
Then, we can re-create rules in Outlook client.