I'm guessing that you are looking at bikes that have a "threadless headset" rather than a "quill stem." The standard Yepp Mini adapter is meant to go on a quill stem. If you want to put it on a bike with a threadless headset (which is the 1 1/8" measurement you're seeing), you'll need a separate adapter:
Yepp Mini Ahead Threadless Adapter at REI.com