Although this thread is a bit dated--I have a solution for the issue (for anyone searching for a fix now like I was).
When you change your text message tone to something other than the default, the notifications for text messages are then treated like a third party app. Henceforth, it gets the signature "triple" vibrate pattern like if it were a Facebook notification or a Snapchat.
To get the original and default single vibrate back, go to phone settings, then under the system header, choose "notifications+actions" and find "Messaging".
Be sure the slider is set to on for "show in action center". Be sure "show notification banners" is checkmarked. And then select "DEFAULT" in the dropdown menu for "Notification Sound". Then be sure "Vibrate" is checked.
This should revert the phone's behavior back to treating the messaging app like it should.
I had just changed my text message tone to a custom one, and when I received a text after the change, I noticed it vibrated three times like a third party app would. I hated it. I want to be able to differentiate what kind of notification my phone is alerting me of without having to glance at the screen every time. So I dug for a solution and this is it. No more scrambling for your phone in your pocket thinking you got a text when it was just an email or something trivial.
*this only applies to Windows 8.1
Can't say the settings are the same for anything older.