So after searching online and testing multiple iPhone 6s' at the Apple store and testing iOS 9.1 public beta the phone does not vibrate when holding down the home button.
The reason I found online has to do with the new M9 processor that has Siri constantly listening. In older phones it would vibrate to indicate that you should start speaking to Siri because she is now listening. This is not necessry with the new iPhone 6s because of the M9 processor.
Perform this test yourself. Hold down the home button and speak right away. Dont wait for Siri to show up on the screen and you will see that she catches every word unlike the older phones that vibrate first before you can speak.
I tested iOS 9.1 public beta and there was no vibration when invoking Siri with the home button. Very clear that it is not a bug other wise it is likely they would have fixed in the beta.
The answer to all our questions is THIS IS A NEW FEATURE and not something that is broken or a software glitch.
I hope this helps you guys.