I had to do a google search on that, had no idea what you were talking about. Those are for taking cuttings of a plant. Put that around a leaf node, fill it with some growing medium, and hope they root. For a while I was wondering just how strong your painkillers were.
Nope,, never used those. The closest I've come is to purposely bury a section of a limb and put a paver over it. In dry weather toss some water on there occasionally. Worked well on a forsythia.
I'd think your challenge is keeping the moisture level right. Not sure how easy crepe myrtles are to root.
I've seen the technique used, but not with a special device. What I saw just looked like an opaque plastic bag wrapped around the twigs & taped in place. That would undoubtedly be cheaper, there were about 10 of those on one shrub. I'll probably be trying something similar next year, in an effort to produce rooted hawthorne cuttings from a very vigorous bush nearby.
That's air layering, we use it for when a cutting most likely won't work. Find a nice branch, scrape the bark off in a circle around where you want the roots to come out, dust it with rooting hormone if you have it, pack wet moss or rooting medium around it and then cover with plastic. Wait a few weeks and check for roots.
Last time it was an air layer from some unknown but utterly delicious variety of orange tree. Also an old variety of rougher but sweeter lemon. Both of them worked but a weed wacker later took out the orange.