This is normal... Avatars can't appear properly until they rez, and they won't rez until your avatar arrived in the new location, have them in your camera field of view, and get all their shape and textures transmitted to your viewer, which takes some time...
I could not reproduce this "workaround" here, and don't see either how it would work at all, since the message for changing your active group got nothing to do with the messages used to get the info necessary to rez other avatars... It more looks like some packets between SL and your computer are getting delayed till the viewer sends another message: probably a network issue (check the MTU, etc: see the other posts about network issues in this forum).
There's nothing to "fix", I'm afraid...