Group Notifications going out to members of other groups

I am using Messaging and Notifications 5.x-1.3 and Mail to Web 5.x-1.x-dev . Everything is working great except that a few users have been mentioning that they are getting notifications from Private groups while others are getting notifications from other moderated groups.( I am not sure if this behavior is restricted only to a few users)

1.I have group content types like discuss, events, bookmark etc
2. Users are by default Autosubscribed to receive notifications
3. Each user, within his account: notifications->content->all group content types have been selected and notifications->groups->all group content types selected

Question:

1. Do I need to to select the group content types under content as well as groups in notifications
2. What is the expected behavior when I select one one or if I select both

Any idea why non-group members are receiving notifications from groups they do not belong to

Thanks