Paul,
Yeah, this is an annoying bug in Facebook right now. Basically, they set a Cookie on the user's computer, and it's not until the next page load that JFBConnect detects it.
Let me look into a possible solution, as it's something we've been meaning to investigate. If we find something soon, we'll post it back here and try to get it in the 4.1 release (due out later this month) as well.
Thanks,
Alex