If the Notezilla notes browser is minimized in the taskbar, then it will popup when you create a new sticky note. If the browser is closed (so the icon appears only in the tray), then the notes browser will not popup when you create a new note.
Also, make sure you have enabled "Always stick new notes to Windows desktop" option in Preferences. To access Notezilla 's Preferences, right click on Notezilla icon and choose Preferences from the menu.