Photo found on Pinterest
Source: Diane Elizabeth's Blog
So these boutonnieres have a magnet built into the back of the flower part and another small magnet that goes on the back of the lapel, holding it in place.
Cheers to the person who figured this one out!
Notes: Check and make sure that nobody has a pacemaker or a problem with magnets before putting these on. If it's a problem, you should be able to pull off/out the magnet and use pins instead.