In my case I usually don't pay too much attention in it as long as I successfully uploaded the new one. If I want to join a signature I'll just tell the campaign manager that it's successful but it may take some time. Usually it take an hour or two (the longest) on my end until it shows on my forum profile avatar especially if that avatar was used for a very long time.
So my question is, is the time that the old avatar is cached for indeterminate, or does it really take a few seconds to update, which means it was just a glitch in my browser?
It really takes long until your browser cache memory recognize the new avatar, unless that avatar was previously cached on your browser. I think it isn't a glitch and this isn't the first time users have encountered the same issue. My advice is just be patient enough.