Use a script timer to run a script to check the status of some field...and when it changes by user 1 setting it, display a dialog.
Not sure what you're really looking for the user experiene to be, but fmChat will let a user chat anorther user (send a notification or actually chat) in Pro and/or Go. And since chats are scriptable you could have scripted actions or FielMaker Server initiate chats / notifications. More here: http://www.seedcode.com/fmchat
If you're going to use Tim's script timer technique I'd add a suggestion to use a FileMaker SQL query to check for notifications (that's what we do in fmChat) instead of a scripted find, which would pull the user's focus off whatever they're doing every time it checks.
Hope that helps.