Rather than having a separate element over the avatar, why not make the default (aka not notified) notification circle a part of the avatar frame itself? That way it won't pop up on a delay as it isn't calling home for a notification or whatever.
Then just have an alternate avatar frame which pops up over it or in the place of the old one which has the red (notified) circle.
I don't know how I'd work it out myself but it's a general idea I suppose.