Trigger type "add to group'' is being retriggered after ANY edit to contact in that group
It's a bit like the custom field issue of a few hours ago.
Make any edit to contact in groupA. If "added to groupA" is a trigger then trigger action is repeated whenever contact is subsequently edited.
In example attached, on March 29th contact completed profile which added them to groupA triggering an email and an activity.
On March 31st contact edited (in this case communication preferences were altered but ANY edit will do), record saved and email and activity were triggered again.