outlook: apply rule to past messages
Here are the instructions for Outlook for Mac 2011 and 2016. 

Basically you have to select the folder or messages you want to apply rules to, then on the Message menu, point to Rules, point to Apply, and then click a rule or click Apply All. You can also right-click or use the toolbar to get to the Rules menu.

The problem I was having is this only works for client-side rules. From my link: "Manually applying rules works only for On My Computer rules. You cannot use Outlook for Mac to manually apply server-based rules." So if you have a server-side rule (which is the default and is probably what you want), you'll have to duplicate it as a client-side rule to get it applied to existing messages.