Diagnosis
The parent unit's alert settings are either turned off, or the unit is in a silent mode like 'Mute Alerts'. It's a separate system from the app notifications.
How to Fix It
On the parent unit's home screen, tap the icon that looks like a bell with a slash (or go to Menu > Alert Settings). Make sure 'Sound Alert' is set to On. Then, check the individual settings: 'Motion Alert' and 'Cry Alert' need to be toggled On. Also, use the volume buttons on the side of the parent unit to raise the alert volume—it's separate from the live audio volume.
If That Didn't Work
The parent unit and camera might be paired in a 'basic' mode that doesn't support smart alerts. Go to Menu > System Settings > Camera Settings and select your camera. Ensure the connection type isn't set to 'Direct Link Only' (which is for when WiFi is down). It should be set to the default mode that uses your home network.
Heads Up
For motion alerts to work, you must have set up an Activity Zone in the VTech Home app on your phone. The parent unit can't create these zones. If no zone is set, the camera won't know what motion to alert for, so it alerts for nothing.