Depends on what you're expecting from the activity. Do you want it to always create a new activity entry every time a group message is sent? Then you'll need to adjust the "Load By" accordingly as that parameter is solely responsible for dealing with duplicates.

Please provide a screenshot of your activity action configuration. If Load By is set to None then it should create an activity entry every time.

The Auto Action that posts the activity posts one activity for each member of the group. How do I set the Auto Action to post just one activity for all the group members?

There isn't a trigger specifically for that, but the below should work.

Global
Triggers: gj_onAfterUpdateGroup
Conditions
Field: Custom > Value
Custom Value: [var1_params_messaged]
Operator: Not Equal To
Value: [var2_params_messaged]

When a message is sent the last time a message was sent is logged to the groups parameters. Using the above you should be able to detect that change and act on it. This would fire just once and avoid the duplicate activity. Otherwise your only option is to use Load By to stop duplicates.