Trigger actions on notification received with IFTTT IFTTT has a notifications channel but unfortunately it does not contain any triggers.

Is there any other way to perform an action when a notification is received?
Is there any IFTTT service that can capture notifications and send them to IFTTT?
How can I use an incoming notification as trigger in IFTTT?

I don't see any reason why IFTTT can't be one of those notification manager applications.
You can use the Android Device IFTTT service:


  https://ifttt.com/android_device


It has "Notification received from specific app" trigger where you can filter the Notification by app name and notification keyword. 

Please beware that the keyword must be a whole word. Trigger won't be fired if you filter "receive" and the notification is "sms received". You must use "received" as a keyword to catch that notification. 

The service also has "Notification received" trigger, that fires for all android notifications.