My Direct Adds appear as quickly as I can change screens so no, it is not normal to take so long. As Owner, I also get a notification that we have a new member in the group. I believe that's the only notice I receive other than, as Bruce said, just going to the Members page and seeing them there. I did set up a "Direct Add" Member Notice so that the new member gets a welcome note - if you also have that set, you might check with the members and see if they received the notice.
Hope you can sort it out.
Barb