Watches and Warning should receive push notifications by default.
Advisories don't have push notifications turned on by default, so you will only see those when you open the app.
If you want to activate push notifications for advisories (which also covers special weather statements), tap the menu (three horizontal lines on the top left) and select the edit location (pencil) icon then tap a location you wish to add advisory push alerts to, and then check the Advisory checkbox.
