One way to get iPhone Push Notifications from Twine
You can use Prowl. Look for them at:http://www.prowlapp.com
You install the app on your iphone. Then use their API to send pushes and you get the notification on your iphone.
What I did was create a simple php web app that used prowl API. So when a twine rule was triggered, I called this web page, the web page called the API with my custom message and prowl pushes the message to my iphone as a notification. Give it a try.
Example Image in notification center:http://i.imgur.com/KBBYT.png
I'm sure there are other ways, but this one seemed good for now. I am just trying to avoid text to my phone