I had this problem too; it probably because the 'features' have slightly misleading names.
The shortcode feature "CallPickupGroup" does not pickup a call from an extension ringing within your group; it picks up a group call (ie a call going directly to the group) when you are temporary disabled from the group.
To obtain what you want, and assuming your groups are 8911-8916 you will have to do either of the following:
(a) For each user, create a user shortcode (lets say **3) and map this shortcode to the feature CallPickupMembers and the Telephone Number field containing the Group Number
(b) Create a short code **3X, feature CallPickupMembers, Telephone number 891N
Then to pickup group 1 dial **31, group 2 = **32, etc.
It would be nice if there was a way of doing CallPickupMembers without a group number to pickup calls from the group you're in, but sadly not.
HTH - Alan