The process did exist, but only for a brief amount of time. It detected a previously running instance of Firefox (through a Mutex, for instance), sent some sort of message (SendMessage, DDE, ...) telling it to open the intended page, and terminated.
What you'd need is for that second process to wait until the page handled in the main process closes. Or better yet, for that second Firefox copy to open the page itself, and in that case you would detect when it has closed.
Unfortunately, for both of these cases you are totally dependent on the program's code, and browsing the forums I didn't find any indication that this can be done
. Maybe you can have a better look ...