A red anger bubble is the clearest sign that two Miis are in a real fight. When you open the event, the angry Mii tells you who they are fighting with and may ask you to help calm them down before they try to make up.
Do not treat every unhappy icon as a full fight. Small lightning, awkward marks, or low mood can mean ordinary friction or sadness instead. Those states may still lower a relationship, but they usually do not follow the same anger-to-cold-war flow.
Player notes suggest these smaller friction states can sometimes be cleared with simple comfort such as patting the Mii, or by bringing another Mii over to trigger a short interaction. That interaction can help, but it can also spread the awkward mood, so treat it as a light fix rather than a guaranteed cure.