Chris
You will get notifications/alerts on the BlackVue app over the Cloud only if your dashcam is ON and connected to the Wi-Fi hotspot that you have saved in Cloud service hotspot settings.
Make sure that you have turned on and properly customized the Push Notifications settings.
You should be logged in on the BlackVue app on your Android/IOS smartphone and it should be connected to the internet to be able to receive the notifications over the Cloud.