iMessage notifications settings that worked for me
Navigate to the following section on your iPhone
Settings > Notifications > Messages
Allow Notification - ON
Time Sensitive Notifications - ON
Lock Screen / Notification Center / Banners - all ON
Banner Style - Temporary
Sounds - Vibrate Only
Badges - ON
Show Previews - ON
Notification Grouping - Automatic
Also please be aware that this application does not tap in directly to the iMessage service. Apple prohibits that as it's their proprietary software/protocol. Phone Link captures what is being sent and received immediately while the Phone Link application is running on your iPhone and sends it to your computer's Phone Link application via Bluetooth. This is why you cannot see historic messages in the Phone Link app and it also cannot take advantage of all the iMessage features.