If there are multiple unread notes, then Notezilla just displays the message with link to View note. Right click on Notezilla icon, choose Notes Browser and click on 'Unread' filter. Read each note (click on each note so that it turns unread).
Once all notes are read, new sticky notes from other contacts will appear right on the desktop.
Basically multiple unread notes are not shown together to avoid annoyance.
Watch this short video for clarity: