This entire process occurs before your phone is even aware of the call to decline it. They are taking advantage of the fact that it takes at minimum a few dozen milliseconds to route a call to your phone.

If you have one of the carriers others have mentioned, they are calling your voicemail directly, completely bypassing your phone.

A few seconds actually. There's quite a bit of features that need to be checked along the path (said as someone working in the telecom industry providing name information).